memling

> I agree, a lightbulb went off for me when it was put that way. I still wonder though, is it just a semantic trick, saying an infinity can't be indexed. I get that if you have all positive decimal numbers, you can't decide what's in the first position, but it feels like asking what's in the last position of a countable infinity - a question that makes no sense. Isn't this why Godel went mad?

Not exactly a semantic trick, and it's not (really) about deciding what's in the first position.

Cantor described two kinds of sets: countable and uncountable. A set S is considered countable if it fulfills one of two conditions: (1) if it is finite, so you can count it by definition, or (2) if there is a one-to-one onto function that maps the natural numbers N to S. This is more or less what I think GP means by "indexing."

"Indexing" as a shorthand for "counting" makes sense, at least for me. I have an array of numbers. Those numbers happen to be positive even integers, but I index them (for sake of convenience) starting from 1. You can draw that on a sheet of paper and people can get it. In fact, you can show them pretty readily that there are no gaps between those numbers; if you have infinite memory, you can index the positive even integers as long as you want, and you can see a one-to-one, onto correspondence.

But if you ask your hypothetical conversation partner to do that with, say, all the real numbers in [0, 1), you can always find a gap between the numbers in their function. You cannot create an index for those numbers. This is much more intuitive than trying to go through the the proof by contradiction,[1] IMO, although obviously it's not rigorous.

Gödel was a paranoid hypochondriac, and I suppose it's tempting to suppose that was partially linked to his mathematical genius. But I actually rather doubt it; he was (apparently) quite lucid when going through his mathematics, and characteristically brilliant.

[1] Here's a stab at it.

Suppose S is the set of all positive even integers. Intuitively S feels like it should be roughly half the size of N, since we're only taking half of them. But what Cantor is saying—I think—is that a function is merely a representation of the numbers. Since f(x) = 2x suffices to map S to N, they are of equivalent "size." You can always index S and figure out what number is at what index x by plugging it into f.

Cantor then proceeded to demonstrate that no such function exists that can map N to the set S of real numbers from [0, 1). He does this by contradiction using a technique called diagonalization.

First, he supposes that some f does exist, that is, for any n in N, f(n) will return a member of S. Then he constructs a number m as follows:

Let g_n(n) be the function that returns the nth digit from f(n). (So, for example, g_1(1) will return the first digit of f(n), g_2(2) will return the second digit of f(1), and so on.) This is where the term "diagonalization" comes from: when you write out the values of S in a grid, g_n(n) will return the digits along the diagonal. Then construct a number m such that its decimal expansion is (g_n(n) + 1) · 10^-n for n in N.

m differs from f(1) in the first digit, and from f(2) in the second digit, and so on down the line—so it cannot be in S. But that can't be right: we assumed from the beginning that we would enumerate all of the values in S by using f, and here is a number that we can construct that f should have enumerated and did not.

> But the idea is that some sets can’t be indexed.

This is a fantastic way to put this. Maybe it's a common way of talking about uncountable infinities, but this is a more intuitive way to lead someone through the problem, I think. Thanks.

Since margin is notoriously low on vehicles, OEMs strive to shave pennies in cost. While I'm also skeptical that we'll have a no-frills EV in the future, too, I suspect it's because monetizing transportation data will outweigh the benefits of reduced cost.

Think "weddinsday," and it might make more sense. I hear that mostly from British-English speakers though.

Vowels were a later addition to many semitic languages as one example. Not sure that it would work so well in tonal or vowel-heavy languages but information is denser in consonants (no real surprise, I guess, given that they outnumber vowels).

> That said, I believe that you understand and agree with my point that scientists have adopted an implicit philosophy.

Before getting to the main body, this was precisely the point I was making in my original response. That is exactly the point. The rest of this is probably wasted electrons, but they're relatively cheap and I've spent them already.

> What exactly bothers you?

That's a good question with which I've wrestled. A couple introductory notes:

Despite the terseness of my replies, I do try to make them thoughtful. My time is limited, and I have found that less is more when writing. I have read what you wrote, but yes, I'm a bit choosy in responding because the content easily spreads well beyond the original intent of my response and my time boundaries. Apologies to Pascal, but I'd have written you a shorter comment if I had the time.

My intent was to correct a few assumptions that you made about me based on the comment—not to convince you that my perspective is correct or to argue that the term philosopher should not be restricted to those who are educated in the field, or even that scientists should be trained in philosophy (although I think the basics of how we approach the human condition would be useful).

None of the following may apply to you personally; I don't assume that they do, and indeed given our conversation suppose that most of them don't.

So, why would it bother me that scientists profess not to be philosophers?

1. Because all people are philosophers (or theologians, or both). That this is trivially true does not mean that people recognize this fact about themselves; scientists are no exception.

2. The scientific method is not a neutral approach to acquiring knowledge; some people suppose that it is, and in so doing they're making a philosophical statement, not a scientific one.

3. The application of that knowledge is obviously not always neutral, and it can have profound consequences.

4. We should generally be more aware of our own lack of neutrality.

5. Science is gradually (or not-so-gradually) replacing our myths and today serves much the same role in answering our questions about who we are, where we came from, where we're doing, and how we're getting there. In other words, science for many people is becoming philosophy (or theology, or both).

6. When scientists fail to recognize this, they may exacerbate the problems we face trying to answer those questions. They could help avoid this, perhaps, by understanding that they are the modern equivalent of high priests (whether they will or no).

This is not to say that science has no role in answering life's big questions; indeed, it does and probably should. But we cannot go from is to ought, or at least history teaches us that doing so is not conducive to human flourishing. Neither is the transition from knowledge to wisdom immediate or obvious. I know you agree with these statements.

The difficulty I have is that many people elide these distinctions with upturned nose, not realizing that they are turning science into scientism. This might be an avoidable outcome.

> Let's start with the idea, "If all A's are B's, then there is no information contained in 'x is a B' that is not also contained in 'x is an A'."

All humans are primates, but not all primates are human: the two ideas are not interchangeable. I'm not equivocating; I'm simply saying that it bothers me when people who implicitly philosophize think or say that they are not.

> That said, it is trivially true that the way that science is carried out demonstrates that they have adopted an implicit philosophy. But that philosophy was mostly developed by scientists themselves, and I've never seen it accurately described by philosophers.

That a truth is trivial does not make it self-evident.

Methodological naturalism is not the same thing as philosophical naturalism, but many people (scientists and otherwise) conflate the two. Whether the philosophy is true or not is a metaphysical question, not a scientific one.

> To the extent that all people are considered philosophers, the claim that person X is a philosopher is meaningless

If ideas had no consequences, this might be true; but since ideas do have consequences, this is probably not true.

> For similar reasons, the historical theological roots of early scientists does not make modern fields like chemistry into branches of theology.

A theologian might disagree with you about this. How would you go about demonstrating that this opinion is incorrect?

> As for science distancing itself from its earlier foundations, there is nothing ironic about it. In fact that act is essential to how science as a field operates.

Scientific progress suggests that we produce more theoretically plausible interpretations of phenomena. As we do that, we often undercut or discard the axioms that produce these new theories: that is what is ironic.

> The comment advocated that scientists should profess to be philosophers.

This context is helpful, thanks.

I didn't advocate anything. I said that it bothers me is that (some) scientists profess not to be philosophers. This is because, in fact, scientists, like all people, actually are philosophers.

> It is because I saw the comment as being part of the genre of people who attempt to raise the status of their field

My field is not philosophy.

> by laying an unwarranted claim to the accomplishments of others.

Neither did I make any claims in my original comment. You seem to have extrapolated quite a lot from a single sentence.

> Philosophy and philosophers do not deserve credit for the accomplishments of science.

The origin of science is obviously philosophical; indeed, Western science is theological in origin (and so is Eastern if you want to broaden your definition of theology a bit). It is equally obvious, if perhaps a bit ironic, that modern science has distanced itself from its earlier foundations.

> Philosophers professing to be scientists has been troubling me more and more the past few years.

Scientists professing not to be philosophers has been troubling me more and more the past few years.

We flip every other utensil to help with this. Genrally works great.

> a merge sort

We use a bucket sort. My wife grudgingly conceded it was faster and doesn't hate doing the dishes as much as she used to (but I still do them most frequently).

Not conclusive, but Luther uses the word Bild in his translation of Genesis 1. That it may have had or acquired the meaning pretty easily given the Bible's formative currency in those years.

FOOF is my favorite. Come for an analysis of Streng's papers and stay for Satan's kimchee.

> Metrology is really fascinating.

It really is. I have some small experience with the industry, an acquaintance I didn't expect to have. The engineering that goes into metrology-grade measurement is incredible.

> Have to point out, though, it seems the one place where everything isn't toxic seems to be (certain forms of) orgnanised religion.

Perhaps what we are seeing is a generalization of religion in which certain aspects of social concern have effectively become religious exercise. This might be a challenging thesis to sustain, but where parallels can be found it might give some broader insight into the present moment.

I've had the luxury, perhaps outside of the first job, of looking for work while I have work. This makes it a bit easier to be targeted in my approach, so it might not work for everyone. But I use a resume to apply for a job, so every job gets a different resume.

At the top of every resume is a job description: a table that lists the company needs and my skills with respect to the requirements--even if I don't have any. Typically it's one page for a hiring manager to compare against the JD and decide whether she wants to look at the canned bullets of my work experience.

My current and prior jobs had a formal application process post offer: I did not go through an online application process or submit a resume to an electronic system until after we'd gone through interviews, etc.

If I find a place I want to work, I make some effort to find out who the hiring manager is for a given position. If I can find an email address, I'll reach out; if not, I look for a mailing address. If I'm really motivated, I'll try to find a phone number.

My experience with this approach has generally been positive: it helps identify good employers, makes, I think, a good impression, and ensures that we don't waste each others' time.

Thanks for passing this along. Carrier's innovations in the work of Bayesian inference applied to history are interesting and definitely worth exploring in greater detail. It's been a fun rabbit hole to go down!

For the interested do you have a set of sources?

> Faithfulness to an imagined "original text" is often asked for, often attempted, but wholly futile.

I think this overstates the case, especially when it comes to the text of the Bible. Thousands of variants exist, but this is precisely because the text was so widely copied. The prevalence of manuscripts and pieces of them dwarfs every other ancient document by orders of magnitude. The abundance provides a means of reconstructing the text with a high degree of probability.

Whether that correlates with truth is of course another question but skepticism about the transmission of the Bible would lead us to much deeper skepticism about every ancient document. Perhaps that's warranted! But it seems like a losing proposition if you are to retrieve anything from written history.

The critical apparatus on the NET Bible is massive. The notes are well worth reading and probably unparalleled for anyone interested in ancient document translation.

Of the unencumbered versions, Young's Literal is popular, although stilted. He used the Textus Receptus and Masoretic Text. Its age means it hasn't kept up with modern discoveries, however. If you have some facility with the original languages, you can find critical editions that highlight significant variants.

Translation is a hard problem, even in modern language. Rendering a figure of speech literally often means finding a comparable phrase in the target language, for example. Word-for-word is not the same as literal!

Entirely possible. I don't know that he was rationalizing as much as passing on accepted wisdom. Undoubtedly escaping depends on more than one variable.

I worked with an older african american many years ago who in his own words grew up in the ghetto. He told me once that, "If we don't beat our kids at home the cops will do it in the street." Not advocating either way, but the perspective stuck with me.

This is simpler but tends to favor the wealthy because such taxes do not impose the same burden proportionately. Moreover the poor rarely invest--I think 401k uptake is only 50% in the US?--and would in present circumstances be challenged to do so. Maybe incentives would change for them under a new system. Another difficulty is that investment income grows over time and governments stand to lose a great deal if they don't tax it.

Relevant: https://www.reddit.com/r/bestoflegaladvice/comments/ki9gb1/i...

The friction stir weld!

> listening to sales had reminded me of my grandmother.

Why?

I had always thought it was just what he said every single time he had to moderate.

> I go looking in the top "file - edit - view - [...]" menus for things that used to be there, find them absent, and then have to go play Where's Waldo in the damn ribbon.

My experience in Word improved dramatically the day I learned the Alt-Q shortcut for just asking for what I want instead of combing through endless menus.