Do you think you could have a stab at answering the questions that were actually asked in the post you replied to?
Split Thread Conspiracy theories about unconventional usage of notation
- Thread starter Steve
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Do you think you could have a stab at answering the questions that were actually asked in the post you replied to?
Mojo
Mostly harmless
W.D.Clinger
Philosopher
Rubbish. No one who understands derivatives would write such rubbish.
If f is a single-valued function of one variable, mapping an argument x expressed in units A to its image f(x) expressed in units B, then the derivative of f is not expressed in units A, and is also not expressed in units B. The derivative of f has units B/A.
And the second derivative of f has units B/A2.
Example. Suppose the position (expressed as the number of meters from some arbitrary origin) of some object at time t (expressed as the number of seconds since some arbitrary origin) is given by a function f(t). Then the derivative of f is the object's velocity (expressed as meters per second), and the second derivative of f is the object's acceleration (expressed as meters per second per second).
Nah, it all depends on context. Like, I might mention that there's a small river at the bottom of my garden and it's about 35" wide. Now, obviously the " there must mean feet, as 35 inches would barely be a stream or even a ditch, whereas 35 feet warrants calling it a river.
Geddit now ??
I can't understand what the highlighted means.
I am unfamiliar with any usage of the term "second derivative" (or indeed "first" or any other ordinal number followed by "derivative") that is not referring to calculus.
If you are referring to calculus, you'll be needing to differentiate with respect to something. So what exactly is this differentiated with respect to in order to get "minutes"?
This reads like half-remembered some terms from some long-ago schooldays, for someone who has forgotten what the terms actually meant.
It is nearly 30 years since I last used differential or integral calculus at university, but at least, since then I have used the concepts at work to understand measurements or simulations and act on them, and I think on a couple of occasions I have actually performed actual analytical integrations or differentiations as part of this.
ETA: Ninja'd by W. D. Clinger
JayUtah
Penultimate Amazing
And it finally clicked: you're trying to replay the Justice Sheen PDF story. Because that story was plausible in one case, you have it stuck in your head now that if you copy-paste something from one document to another, it might change some of the characters. And once again faced with having typed something wrong, not realizing it until too late, and not wanting to admit to any conceivable error, you're grasping at that straw again.
I've been trying to figure out why you didn't just screen-shot the WhatsApp conversation to try to prove your point. Why did you have to copy from WhatsApp, paste it into a different program, and screen-shot that program? And the answer is that this is what had to happen in the Sheen story, so copy-pasting is what you think you have to do to make a credible story in this case.
Very often as a knowledgeable skeptic dealing with uninformed and misinformed people, you have to figure which of an infinity of wrong ideas they have in their head. Someone who knows how character encodings work in computers has the one right idea. But someone who doesn't know anything about that bases their understanding of what happens behind the scenes when you copy and paste on who-knows-what.
Here is the letter R. What is actually stored in the computer memory for that letter in this post? It's an 8-bit number, 0x52 in hexadecimal or 01010010 in binary. Why that particular number and not, say, 42? Because we've agreed internationally for decades that the binary value 01010010, interpreted as a letter, will be the uppercase letter R. We call that agreement ISO/IEC 8859-1, which comes from the old ASCII standard from the days of the teletypes. The assignment of these 8-bit values to stand for letters and symbols in a computer's memory, or in digital communications, is called a character encoding. You may have seen other names for similar encodings such as UTF-8 or Unicode.
So back in the day when you were misusing the way primes notation was supposed to indicate time, a teletype that received the binary value 01010010 over its bulky, noisy, slow serial digital connection would put in motion some physical mechanism that would result in a metal type for R being positioned between a hammer and an ink ribbon. Then the hammer would fire, and you'd get an R-shaped ink smudge on the paper.
In the days of primitive computer terminals, the terminal received 01010010 over a slightly better serial line, and this told electronics to aim an electron gun in a certain way to paint a picture of an R in green phosphor. Go watch the old Andromeda Strain. They use this kind of terminal extensively.
We've improved on that a bit. How are you able to see an actual letter R in your browser, in this post, as you read it? Your browser reads 01010010 out of the computer memory in a programmatic context that tells it it's supposed to interpret it as a letter. Then it goes to the data for the typeface you've chosen for your browser and looks up the glyph for 01010010. The glyph is simply the set of instructions that tells the pixel-painting portion of your browser how to make an uppercase R, in that typeface, in pixels.
Here's R in the default typeface. Here it is, R, in a different typeface. And a third: R. You see different pixels painted in each case because the glyph is different in each typeface. But if you could magically peek into your computer's memory where it's holding the text of the post—the binary values, not the picture of the post that your browser has painted out of its typefaces—you'll see 01010010 in all three cases. By default, the browser translates binary values into the proper glyphs using the IEC 8859 encoding.
What's stored for 𝕽, a stylized uppercase R used in mathematics? In this case, not 01010010. Here we've switched encodings (and told the browser so) to use Unicode.1 We need more bits for that, because the encoded value for this character is 0x1D57D in hexadecimal. Not only is it looking up a different glyph, its underlying representation is different from just plain R. It is a different character with a different meaning.
So when you copy and paste, what happens? The glyphs don't get copied. The picture doesn't get copied. The encoded values stored in the underlying bytes get copied. In WhatsApp's program memory, 01010010 for R is packaged up and sent to, say, Firefox where it appears in that program's memory as 01010010. It may look different because Firefox is using a different typeface than WhatsApp to paint the pixels. But the underlying encoded characters do not change.
Put more applicably, if an encoded text byte is 0xBA (the symbol º), copy-pasting it into another program won't change that encoded byte to 0x22 (the basic double-qoute, ").
So what made that happen in the Justice Sheen report on Herald of Free Enterprise? JimOfAllTrades already covered that. What's stored in the PDF file for the symbol º as it appears in the report? Not an encoded character. That PDF is a scanned document. Someone put the paper report on a scanner, and the scanner took a picture of the symbol. That picture is what is stored in the PDF. Sure, your browser—and other programs—know how to receive the binary description of the picture and turn it into pixels for you. But it's just doing the same thing dumbly for every kind of picture: cats, scanned text, people's naughty bits.
Copy-pasting from this works entirely differently. As Jim notes, it's a bit of a software miracle that it can happen at all. When you select and copy the picture of the text, the PDF viewer program is furiously trying to interpret bits of the picture as letters, the way our eyes and brain do. Once it has done so, the data that goes into the clipboard is not the picture, but the encoded value for the character the program thinks the picture shows. If the picture looks like an R, the program puts 01010010 into the clipboard memory. But because this process isn't perfect, sometimes the picture of a º might look more like a picture of a " to the algorithm, so it stores 0x22 instead of 0xBA. Then at the destination, the ordinary character rendering process I described above paints the glyph for " instead of for º because that's what got (wrongly) encoded as the result of the picture-interpreting part of the PDF viewer. The destination has no way of knowing any different.
But wait, there's more.
When you type the " key on your computer, a binary signal for that keystroke is being given to whatever program has the keyboard focus at that moment on your computer. Most ordinary keystrokes get translated into the encoded character appropriate for that key sequence. So when I hold down the Shift key and press the R key, the binary value 01010010 (for uppercase R) gets delivered to the program as data that it's supposed to do something with. When I hold down Shift and press the key with the single and double quotes, the program gets 00100010, the code for a plain old double-quote.
So what does it do with it? Depends on the program. The vast majority of programs (including WhatsApp and Google Mail) simply add that character code to the current place in the document without further fuss. And then the glyph-painting part of the program paints some pixels in the right place on the screen according to what the typeface glyph says the R should look like.
But some programs try to be clever. A word processing program like Microsoft Word wants to make documents as pleasing as possible. Typographers know that plain old straight up-and-down double quotes " don't look good in type. We want “pretty” marks, where the open-quote and closed-quote symbols (single or double) are slanted, curled inward, or possibly inverted. But we don't want to make the writer hunt around for the right way to do it. “ and ” aren't just alternate glyphs for 0x22. They're completely differently encoded characters. If you look into the computer memory for this post, you won't see 0x22 surrounding the word pretty.
So when Word (and other Microsoft programs) see 0x22, they don't just dump that character into the data they're accumulating for your document. Word tries to see whether you're at the beginning of a sentence or the end of a sentence and instead of storing 0x22, it will store 0x201C or 0x201D instead, representing the encoded character of the open- or closed-double-quotation. Those are entirely different characters than 0x22. It's helping you make your document look more pretty without you having to try too hard.
If you copy and paste from Word, it copies those binary codes, not the 0x22 you originally typed. If you copy 0x22 into Word (as opposing to pressing the keys for "), you just get the plain glyph ". Later, other algorithms in Word might kick in and do the translation, replacing 0x22 with 0x201C or 0x201D. And if you leave the 0x22 in there and copy it out of Word, the translation into the typographic characters does not occur.
WhatsApp doesn't do any of this when you type. Text-entry widgets in Outlook for Web, Google Mail, or this forum don't do any of that. None at all. You only get that pattern of encoded typographical quote marks (not 0x22 or 0x27) when you type into Word. The statement you purport to be from a mathematician was typed into a Microsoft product, which then mangled it.
At my company we vacillate between turning the helpful rewrite features off or leaving them on. We want them to do their thing when we're writing plain English documents. But we don't want them to happen when we're typing technical expressions or symbols. At best they get in the way, and at worst they silently rewrite things incorrectly.
And we never, ever, ever use a single-quote followed by a double-quote, '", to approximate a forward triple prime. You always type three single-quotes, ''', or three backticks, ```, for a reverse triple prime. That's where you slipped up. Your "mathematician"—who clearly exists only in your head for the purposes of this thread—made a cardinal mistake. Your Microsoft typography slip-up just helped us see it more clearly.
So there's the full debunking of your, "It just copied that way, I swear," ploy. This isn't the same situation as the Sheen report, and you don't know enough about how computers work to lie effectively about how your symbols got botched up again.
____________
1 I'm aware that the single-byte encodings for Unicode are identical to the single-byte encodings for IEC 8859-1, and that likely the browser is just always using Unicode.
Furthermore to this:
" ...the usual - and much more normal - number of hours it takes a ship to sink below the surface of the water."
What does this phrase mean? Is there a "usual time for ships to sink below the water"? From when does one measure it? Launch? Start of the trip? When the first trouble is reported? Abandon ship is announced?
What dataset is used?
All ships throughout history?
Ships launched in the 20th Century? Do you include the merchant ships sunk in convoys?
Passenger ferries that have sunk?
JayUtah
Penultimate Amazing
People here do know better than you, and unlike you they can demonstrate that knowledge instead of inventing ever more absurd stories. You refuse to concede.
JayUtah
Penultimate Amazing
No. You wrote
The ship sank in 35".
with no context or further explanation. Since you wrongly thought ″ meant minutes, you have no reason to believe that people thought you were talking about minutes (or any other unit) of time. It correctly means either thirty-five inches of distance (most common) or thirty-five seconds of time (long outmoded usage), both absurd in context. And since your latest story is that your misuse is both minority and unofficial, there is no information—contextual or otherwise—that would lead any reasonable person to understand your intent. As a result they properly laughed at you.The telltale is when you read the correction and immediately started using ′ properly to mean minutes (of time). You didn't acknowledge being corrected, but you silently started doing the right thing. Only much later, when you had to account for using both ″ and ′ to mean minutes of time, did we get the whole story about using symbols interchangeably and having to properly understand things "in context."
You screwed up, tried to sneak in a correction unnoticed, and then had to invent story after story and deploy one straw man after another to avoid having to concede that you made a mistake.
No, none of this is correct. This is the opposite of how the whole system of primes notation works. And now you're misusing the word "derivative" as well.
Just stop trying to be smart. You're not fooling anyone.
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JayUtah
Penultimate Amazing
Like every other attempt she's made to pontificate on a technical subject. She's throwing around sciency- and mathsy-sounding words in the hope that someone will think she's smart. It's pure technobabble.
The concept of a derivative from calculus is only tangentially applicable (pun intended), and only because we use primes notation to mark the derivatives of a function. For some function 𝑓(x), its first derivative is notated 𝑓′(x), its second derivative 𝑓″(x), and its third derivative 𝑓‴(x). When we have to write them in IEC 8859-1, we use single-quotes only:
Code:
f'(x), f''(x), f'''(x);Someone who types '" (i.e., a combination of single- and double-quotes) to approximate a triple prime has revealed herself not to be proficient or experienced in typing math stuff on computers.
There is also the notion of a derived unit. SI has the Sacred Seven basic units, the seven extents we cannot break down into simpler physical phenomena. They are time (seconds, s), length (meter/metre, m), mass (kilogram, kg),[1] electrical current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd). Derived units are combinations or special applications of the basic seven units. Torque (newton-meter, N⋅m), for example, is derived from force and distance, and force (newton, N) is itself a property derived from mass, distance, and time.
Deriving properties such as force and defining the units to measure them very often implicates differential calculus, but this is merely accidental. A derived unit in SI need not have arisen necessarily from the calculus derivative of a function. It's just two different uses of the same word, and it has nothing to do with subdividing units into smaller units according to some system, ancient or modern.
Neither of those applies to her gobbledygook. It's just as incoherent and (insofar as it is intelligible) just as wrong as her comical attempt to explain metacentric height. Pure ignorance cloaked in narcissistic bluffery.
______________________
[1] The kilogram instead of the gram because SI is a subset of the whole metric system used for science and engineering, and the process of normalizing for formal consistency requires us to use kilograms here instead of the unprefixed unit.
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Elvis666
Muse
You are correct. Paris, Tennessee is not is capital of France.
Sent from my SM-G950U using Tapatalk
JayUtah
Penultimate Amazing
Obviously she's alluding to the what she's copied from Björkman: the incorrect notion that a ship that rolls past its critical roll angle will turn turtle completely and float for several hours.
But really—as your questions bear out—no two ship sinkings are alike in all their particulars. Some do float for hours. Some sink in minutes, like Vasa and Lusitania. The orientation of the ship in the water is irrelevant. There is literally only one factor that determines how fast a ship sinks: the rate at which buoyancy is lost.
So the first problem with Vixen's proposal is tying her notion of context to a variable that's frankly all over the map. There is no "customary" time it takes for a ship to sink, and it's patently absurd to claim it's always on the order of hours.
But the biggest problem is the utterly ludicrous idea that symbols change which units they stand for based on anything like "context," especially a context that's merely implied, or based on such variable, subjective concepts as what is "customary." This is completely antithetical to the whole practice of measurement and notation as it has evolved over literally thousands of years.
The best kind of notation is self-identifying. Leonardo includes a scale in his drawing of the Vitruvian Man, in diti and palmi (4 diti to the palmo). And the symbols di and pmi in some other Italian texts of the period always clearly refer to diti and palmi, respectively, and cannot reasonably be confused. 5 pmi is always "cinque palmi," never "cinque piedi" or "cinque diti." Closer to home, ft never means anything but feet. kg never correctly means anything but kilograms. They can't. We love self-identifying abbreviations.
Vixen is quite okay with ′ never meaning anything but feet of distance and ″ never meaning anything but inches of distance. And because that is correct, and these symbols have fixed meanings, we can dispense with yd. But it illustrates exactly why we can never reuse ″ to mean, say, feet. The symbol is not self-identifying, and allowing it to variously mean this or that depending on an unsure "context" leaves the system entirely useless. It's already bad enough that ″ means both seconds and inches.
The trend even 200 years ago was to get rid of ambiguous symbols. º once did also stand for hours in the primes notation for time, but it was quickly pushed aside in favor of h for hours. (Vixen's head-canon "mathematician" is just plain wrong.) And in some notations of that same period, a superscript d meant degrees of arc, precisely so that º wouldn't need any context in order to know whether you meant time or angles. Today the convention is that º only ever means degrees, whether of temperature or of arc. But that's still distasteful to those of us who really need precise notation, so for temperature we still require the scale notation, º F or º C. º by itself formally can mean only degrees of arc.
Adding ambiguity to ′ and ″ isn't cricket. Just because they aren't self-identifying doesn't mean they can take on any meaning. It means instead that their nominal meanings must be respected as a matter of edict. Adding maximum ambiguity by allowing implied contexts to change which units those symbols mean is as far away from science, commerce, and engineering as you can get. Whether for time, angles, or distance, the indulgence of non-self-identifying symbols is thoroughly tied to the inviolable principle that these symbols never take on different meanings. You learn once that ″ means seconds of arc (or, anciently, of time), or inches of distance, and that never changes. The usefulness of the system for any purpose relies upon this.
But what a flip-flop we're seeing today. In order to give us a story so vernacular we couldn't refute it, Vixen tells us ″ for minutes was something people used informally at her school, and that you knew you shouldn't use it for anything that an examiner was going to see. That means those folks knew it went against some kind of rule. But now by flinging around "second derivative" and other inapplicable concepts, she's trying to go back the other way. Now she's trying to say there is some kind of formalized basis for using ″ for minutes, something that someone somewhere would have written down, something for which there should be evidence of its wider use. And if that's the case, why wouldn't the examiners at her school have accepted it on homework?
She just can't help herself. It's just one incompatible story after another. And for some reason she can't grasp that this is conclusive evidence for us that she's making stuff up. She can't keep the story straight.
junkshop
Otto's Favourite
Waffle, umbrage taken,
<FX: Unloads bales of straw>
My school accepted Paris, Texas as a correct answer to the question. Obviously this is correct when read in the context of Wim Wenders being an European film focus-puller (which my school accepted as interchangable with director, but you wouldn't know that: I went to a different school, in
<FX: adopts a smug pose, and accidentally sets fire to the mountain of straw with sparks of erroneous notation>
I totally meant to do that. Anyone that suggests that I didn't is just a meanie.
MarkCorrigan
Героям слава!
So Vixen, are you still claiming that you are perfectly willing to acknowledge your errors when they are pointed out to you?
I Am The Scum
Philosopher
- Joined
- Mar 5, 2010
- Messages
- 5,796
Alright. That's my claim. Lyon is a capital city. Has been for decades. Please correct the error, as you said you would. Prove me wrong.
Vixen
Penultimate Amazing
As I keep saying that is how primes appear on WhatsApp. Here is a screen print of the original WhatsApp message so please stop falsely accusing me of wrongdoing.
Vixen
Penultimate Amazing
If you would care to join us on the Sinking of the Estonia thread, it will become readily apparent to you that for a ship to sink without trace* in less than an hour is most unusual. When a boat capsizes, it generally floats upside down (think ordinary rowing boat or kayak) If it is torpedoed, as in war situations, the bow, stern, hull or beam will often be seen sticking out o the water for anything from five to eighteen hours up to as long as five days, as happened with a similar ferry to Estonia a couple of years earlier.
*I.e., no visible trace of it on the sea surface.
Vixen
Penultimate Amazing
As a hard-headed realist I have zero problem in correcting errors.
I imagine that is well and truly debunked on that thread. Probably including the obvious point that not all vessels are equal. My daughter kayaks, sometimes with a sea kayak, that or a surfboard will not sink even if upside down. A roll-on roll-off ferry, with a vehicle deck and consequent large structural gaps to accommodate the speedy entrance and exit of commercial vehicles is going to be far more susceptible, especially if something has happened to the doors protecting these gaps into the vehicle deck.