Harvard class fails (1964) Literacy Test
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Harvard class fails (1964) Literacy Test
Exactly what it sounds like, a Harvard Professor decided to give his class the infamous 1964 literacy test to vote. Total failure, mostly because of the time limit that gives each question 20 seconds. Plus deliberately vague and confusing directions that can always be interpreted as a fail, and traditionally one wrong question failed the test.
Video
Daily Mail Article including the test.
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Daily Mail Article including the test.
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Re: Harvard class fails (1964) Literacy Test
Wow...that test is fucked up.
Ok this test is definitely a rigged one. Most of the questions made sense but several did not...and I'm reasonably sure numbers 2, 3 and 4 are trick questions.
Um, what? How do you draw a line around anything? It's called a circle...1. Draw a line around the number or letter of this sentence.
Ok I can see how that would be confusing to some people. Would be easier to say "Circle the first letter A in the line".5. Circle the first, first letter of the alphabet in this line.
What the hell?In the first circle below write the last letter of the first word beginning with "L"
Ok this test is definitely a rigged one. Most of the questions made sense but several did not...and I'm reasonably sure numbers 2, 3 and 4 are trick questions.
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Re: Harvard class fails (1964) Literacy Test
Are we looking at the same test? Just what is a trick in "Draw a line under the last word of this line."? Just draw a line under the last word. Same with #3 which tells you to cross out the word with most letters in it and #4 that has you circle the shortest thing that qualifies as a word. Really, I see no problems with most of the questions up until you get to 11 which I find a bit confusing.Borgholio wrote:Ok this test is definitely a rigged one. Most of the questions made sense but several did not...and I'm reasonably sure numbers 2, 3 and 4 are trick questions.
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Re: Harvard class fails (1964) Literacy Test
If you scroll down to the bottom of the article, it specifically notes that the test is created so that examiners could intentionally interpret each answer as wrong, hence the gratuitous mixing of 'circle' and 'line' and so forth.
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Re: Harvard class fails (1964) Literacy Test
so essentially this test was a way for the racist politicians to say that they gave blacks a fair chance for voting without actually giving them a fair chance, am I right?
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Re: Harvard class fails (1964) Literacy Test
Was this a literacy test that was employed in the same way like voting restrictions (to screw over minorities)?
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Re: Harvard class fails (1964) Literacy Test
I read that as well I just don't really see it. I mean sure, the questions are lose enough that in theory you can misinterpret them to fail someone. But it's not something you can do without trying really hard. You basically have to put in effort to intentionally cheat the people taking that test. At least I would. Otherwise it's really not that hard a test.Elheru Aran wrote:If you scroll down to the bottom of the article, it specifically notes that the test is created so that examiners could intentionally interpret each answer as wrong, hence the gratuitous mixing of 'circle' and 'line' and so forth.
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Re: Harvard class fails (1964) Literacy Test
Yes the literacy test was typically something that could be ordered at the polling place. Also if a polling place was giving them out to everyone the minders could simply toss the failed tests of those they wanted to vote and told them they passed. It's not like these were conducted by blinded and independent professional test markers.Thanas wrote:Was this a literacy test that was employed in the same way like voting restrictions (to screw over minorities)?
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Re: Harvard class fails (1964) Literacy Test
Yes. Before the Voting Rights Act of 1965, this test and others like it were applied in Southern states as a prerequisite for voting, and were deliberately rigged.Thanas wrote:Was this a literacy test that was employed in the same way like voting restrictions (to screw over minorities)?
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Re: Harvard class fails (1964) Literacy Test
I interpreted rather obtusely in places:
If you're taking this test it's obvious the test giver is out to get you, making it more likely you'll look for clever hidden tricks, which if they aren't there you'll answer wrong for assuming too much, but if you answer normally you could be wrong for assuming the instructions were implying the "normal" or "obvious"thing to do instead of the most literal interpretation (as hinted at by the "do nothing more, nothing less" part of the instructions).
Code: Select all
1. Can't draw a line "around" something
2. ok
3. In line 3 of the test, or in the literal string "word" of which there is only one occurrence, or literal string "this line" which doesn't have a single longest word. Also, "cross out" would allow marking wrong an answer that used a "strike through" rather than two intersecting marks.
4. combination of questions 1 and 3
5. The first letter of "The Alphabet" is "T", the first occurrence of which is in "the". Or they could mean "A"
6. Oddly phrased. "one inside the other" only really tells you what to do with two of the three circles to be drawn. Best solution I can think of is three concentric circles.
7. ok
8. Similar to question 5.
9. Only avoids the ambiguity of 5 and 8 by not having a possible valid solution for one interpretation (unless you cross out the first "e" in question 10)
10. Either T for "last" or A for "Louisiana" (first word starting with "L" on the test) Or "A" for La (first L word in the dictionary)
11. "the number" implies a unique solution, but striking any of the four right zeros would be correct.
12. ok
13. ok, so long as the line doesn't have to be straight.
14. Straightforward if you assume you're supposed to use the alphabet under the question; otherwise it could be the a in "and" after ' "h" ' and the b in the alphabet after ' "j" ', or go back to the start of the test and find the first occurrences of "h" and "j"
15. Doesn't specify if the letters should be mirror imaged. Could also mark wrong if you forgot the dot following the half note. Or did you think it was a lower case d and the article would exclude the dot? Or does it?
16. seems ok
17. Could be 32; but there are an infinite number of solutions possible
18. "12" would fill the gap, but the question asks what comes next; so the answer could be "18"
19. seems ok
20. could be "backwards" or "sdrawrof", also doesn't specify if letters should be mirror imaged
21. ok
22. ok
23. seems ok
24. "MOM" would work. some words like NOON would appear to be fine unless you go for mirror imaging
25. standard "gotcha" question; "the" is repeated, but when rushed your brain will tend to auto-correct the extra 'the'
26. I see three interpretations: Q in square, H in "tHe fourth word", O in Louisiana (fourth word on the test)
27. seems ok
28. ok
29. doesn't specify which word to start with. and is it implying to write in cursive other than the printed words?
30. doesn't define interlocking or part. do they mean a 5 circle venn diagram, or 5 circles intersecting at one point, or 5 circles intersecting at EXACTLY one point, or 5 circles sharing 1 "part" of a circle (origin, radius, diameter)? (only part 5 distinct circles could share in the same location would be the origin)
Last edited by Jaepheth on 2014-11-12 07:48pm, edited 1 time in total.
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Re: Harvard class fails (1964) Literacy Test
Well sure the answer SEEMS easy for most of these. Trouble is they are so vague that a racist asshat could choose to interpret the question differently and fail you. I mean yeah I could get *an* answer for most of these at a glance, but they are not as clearly defined as 2+2= ?.Purple wrote:Are we looking at the same test? Just what is a trick in "Draw a line under the last word of this line."? Just draw a line under the last word. Same with #3 which tells you to cross out the word with most letters in it and #4 that has you circle the shortest thing that qualifies as a word. Really, I see no problems with most of the questions up until you get to 11 which I find a bit confusing.Borgholio wrote:Ok this test is definitely a rigged one. Most of the questions made sense but several did not...and I'm reasonably sure numbers 2, 3 and 4 are trick questions.
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Re: Harvard class fails (1964) Literacy Test
Mind if I disagree and point out where?Jaepheth wrote:I interpreted rather obtusely in places:
Of course you can. The term line includes both strait lines and curves.1. Can't draw a line "around" something
Where are you getting the "literal string" thing from? Seriously, I am not sure what kind of thought process produces that. But the question clearly says to cross out the longest word in that line, meaning the word with most letters in the particular line of text.3. In line 3 of the test, or in the literal string "word" of which there is only one occurrence, or literal string "this line"
Yes it does.which doesn't have a single longest word.
Cross
out
the
longest
word
in
this
line
Count the number of letters. The word "longest" is the longest word in the line.
That I can agree with. It's the only plausible thing you have said so far.Also, "cross out" would allow marking wrong an answer that used a "strike through" rather than two intersecting marks.
The examiner would have to be intentionally obtrusive to make such a conclusion as it violates the basic structure of the English language. But again, I can see it happening if the guy was a moronic dick bent on screwing someone over.5. The first letter of "The Alphabet" is "T", the first occurrence of which is in "the". Or they could mean "A"
You missed a more important thing. The only way to get the number shown to be bellow (not bellow or equal) to 106 would be to strike through two zeroes or the one. Removing just one zero gives you 106 exactly.11. "the number" implies a unique solution, but striking any of the four right zeros would be correct.
Why should it have to be?13. ok, so long as the line doesn't have to be straight.
Why would you even consider that option though? If someone tells you to write a word backward you will just write it backward, as in reverse the order of the letters. Why would anyone consider that option at all? Like many of the other conclusion it really makes no sense if you refuse to suspend basic intelligence and understanding of how language works.15. Doesn't specify if the letters should be mirror imaged.
I am going to say yes.Could also mark wrong if you forgot the dot following the half note.
What do you mean by infinite number of solutions? I can only see 32. It's the kind of basic question you see on online IQ tests these days.17. Could be 32; but there are an infinite number of solutions possible
I'll give you that. But to be perfectly honest I do not see anything dishonest about using such a question if the goal is to test reading comprehension.25. standard "gotcha" question; "the" is repeated, but when rushed your brain will tend to auto-correct the extra 'the'
I am continually confused as to how you are coming up with these rather far fetched ideas that one is supposed to answer a question by using stuff outside of the context of the question it self. I mean, I can imagine a racist redneck or something drawing the same conclusions on purpose to screw people. But it literally takes not just suspending but outright struggling against ones intelligence to come up with these things. I would actually have to struggle and put in a hell of a lot of effort into finding these things because as far as ideas go they just do not make sense to a sane mind.26. I see three interpretations: Q in square, H in "tHe fourth word", O in Louisiana (fourth word on the test)
I'll give you that. And I do believe that they do indeed expect you to mix cursive and print just to screw with you.29. doesn't specify which word to start with. and is it implying to write in cursive other than the printed words?
Does it have to? An interlocking part is a part where two or more objects interlock. As in, a 5 circle venn diagram with one single area common to all 5 circles and no other intersections. Now admittedly I have not tried to draw this so I do not know if it is in fact drawable. But that's not what you addressed so it does not matter in the context of this discussion.30. doesn't define interlocking or part.
That's the thing though. In order to interpret these in any way other than what is obvious you have to deviate so much from both logic, sanity and the spirit of the english language that I do not believe it could be done by some undereducated racist asshat. You have to actually be very smart and dedicated in your efforts to break logic in order to do it. Although I can imagine they got cheat sheets or something. In fact, even with what was written by Jaepheth in front of my eyes I still find it very difficult to even analyze how he made the conclusions he did, let alone come up with any of mine.Borgholio wrote:Well sure the answer SEEMS easy for most of these. Trouble is they are so vague that a racist asshat could choose to interpret the question differently and fail you. I mean yeah I could get *an* answer for most of these at a glance, but they are not as clearly defined as 2+2= ?.
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Re: Harvard class fails (1964) Literacy Test
I don't know how it is elsewhere, but growing up in the South I'd hear a "joke" every other week that relied on some bullshit pedantic word play. Hence the actively looking for extremely literal readings of the questions that would yield an answer other than what a reasonable person would expect (because the obvious answer is obviously a trap).
As for the infinite solutions to 17 & 18; I just meant you can put nearly any number you want in there and calculate a Lagrange polynomial that produces that sequence exactly (Doesn't have to be a polynomial, I've seen some where there's multiple possible single order answers). For very simple sequences it's fairly obvious what the question's author was going for (but that's a cultural bias for simplicity) but up the complexity a little bit and you're left guessing what the author's thinking.
As for the infinite solutions to 17 & 18; I just meant you can put nearly any number you want in there and calculate a Lagrange polynomial that produces that sequence exactly (Doesn't have to be a polynomial, I've seen some where there's multiple possible single order answers). For very simple sequences it's fairly obvious what the question's author was going for (but that's a cultural bias for simplicity) but up the complexity a little bit and you're left guessing what the author's thinking.
Last edited by Jaepheth on 2014-11-12 08:47pm, edited 1 time in total.
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Re: Harvard class fails (1964) Literacy Test
Consider that you have roughly 30 seconds to read and answer each question, had the test suddenly sprung on you with no prep time, and the consequence of failure is that you lose a basic right. Does it still seem so straight forward?Purple wrote:Mind if I disagree and point out where?Jaepheth wrote:I interpreted rather obtusely in places:
Of course you can. The term line includes both strait lines and curves.1. Can't draw a line "around" something
Where are you getting the "literal string" thing from? Seriously, I am not sure what kind of thought process produces that. But the question clearly says to cross out the longest word in that line, meaning the word with most letters in the particular line of text.3. In line 3 of the test, or in the literal string "word" of which there is only one occurrence, or literal string "this line"
Yes it does.which doesn't have a single longest word.
Cross
out
the
longest
word
in
this
line
Count the number of letters. The word "longest" is the longest word in the line.
That I can agree with. It's the only plausible thing you have said so far.Also, "cross out" would allow marking wrong an answer that used a "strike through" rather than two intersecting marks.
The examiner would have to be intentionally obtrusive to make such a conclusion as it violates the basic structure of the English language. But again, I can see it happening if the guy was a moronic dick bent on screwing someone over.5. The first letter of "The Alphabet" is "T", the first occurrence of which is in "the". Or they could mean "A"
You missed a more important thing. The only way to get the number shown to be bellow (not bellow or equal) to 106 would be to strike through two zeroes or the one. Removing just one zero gives you 106 exactly.11. "the number" implies a unique solution, but striking any of the four right zeros would be correct.
Why should it have to be?13. ok, so long as the line doesn't have to be straight.
Why would you even consider that option though? If someone tells you to write a word backward you will just write it backward, as in reverse the order of the letters. Why would anyone consider that option at all? Like many of the other conclusion it really makes no sense if you refuse to suspend basic intelligence and understanding of how language works.15. Doesn't specify if the letters should be mirror imaged.
I am going to say yes.Could also mark wrong if you forgot the dot following the half note.
What do you mean by infinite number of solutions? I can only see 32. It's the kind of basic question you see on online IQ tests these days.17. Could be 32; but there are an infinite number of solutions possible
I'll give you that. But to be perfectly honest I do not see anything dishonest about using such a question if the goal is to test reading comprehension.25. standard "gotcha" question; "the" is repeated, but when rushed your brain will tend to auto-correct the extra 'the'
I am continually confused as to how you are coming up with these rather far fetched ideas that one is supposed to answer a question by using stuff outside of the context of the question it self. I mean, I can imagine a racist redneck or something drawing the same conclusions on purpose to screw people. But it literally takes not just suspending but outright struggling against ones intelligence to come up with these things. I would actually have to struggle and put in a hell of a lot of effort into finding these things because as far as ideas go they just do not make sense to a sane mind.26. I see three interpretations: Q in square, H in "tHe fourth word", O in Louisiana (fourth word on the test)
I'll give you that. And I do believe that they do indeed expect you to mix cursive and print just to screw with you.29. doesn't specify which word to start with. and is it implying to write in cursive other than the printed words?
Does it have to? An interlocking part is a part where two or more objects interlock. As in, a 5 circle venn diagram with one single area common to all 5 circles and no other intersections. Now admittedly I have not tried to draw this so I do not know if it is in fact drawable. But that's not what you addressed so it does not matter in the context of this discussion.30. doesn't define interlocking or part.
That's the thing though. In order to interpret these in any way other than what is obvious you have to deviate so much from both logic, sanity and the spirit of the english language that I do not believe it could be done by some undereducated racist asshat. You have to actually be very smart and dedicated in your efforts to break logic in order to do it. Although I can imagine they got cheat sheets or something. In fact, even with what was written by Jaepheth in front of my eyes I still find it very difficult to even analyze how he made the conclusions he did, let alone come up with any of mine.Borgholio wrote:Well sure the answer SEEMS easy for most of these. Trouble is they are so vague that a racist asshat could choose to interpret the question differently and fail you. I mean yeah I could get *an* answer for most of these at a glance, but they are not as clearly defined as 2+2= ?.
Re: Harvard class fails (1964) Literacy Test
I interpreted that one to be "...when making the number (written) below (equal to) one million."Purple wrote:You missed a more important thing. The only way to get the number shown to be bellow (not bellow or equal) to 106 would be to strike through two zeroes or the one. Removing just one zero gives you 106 exactly.11. "the number" implies a unique solution, but striking any of the four right zeros would be correct.
Since every other use of "below" in the test is to point to whatever doodle is under the question.
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Re: Harvard class fails (1964) Literacy Test
Yes, precisely. Officially, the idea was that if you couldn't provide proof of at least a 5th Grade education (which effectively meant a high school diploma, from a white school) you could still vote by passing the test. But that was always a rigged deck, these tests and poll taxes were how the South disenfranchised minority voters for decades. Until the Voting Rights Act in the sixties, which abolished these tests and taxes, and required the states to submit all changes to their voting laws to Congressional approval. This same VRA that was recently overturned by the Supreme Court, allowing the flowering of voter ID laws and mass disenfranchisement.Thanas wrote:Was this a literacy test that was employed in the same way like voting restrictions (to screw over minorities)?
The Louisiana Test enjoys a special notoriety, it was pretty much first in the show-and-tell of "this is why we need the Voter's Rights Act." Until today, I'd never seen the actual text of it, though I'd known that applicants had exactly ten minutes and a single wrong answer invalidated the whole thing. Like the "write backwards, forwards." one. There's at least four possible answers, backwards, sdrawrof, and the mirror of each. And with that much choice and zero chance of clarification, whatever answer you give is gonna be the wrong one, because that's what the proctor will say. It's a test that can't be passed, but is supposedly the minimum standard for proving you can match a 5th Grader's literacy.
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Re: Harvard class fails (1964) Literacy Test
Right. It's like, a fifth grader could comply with the test, and could conceivably answer the questions... but that "a single wrong answer invalidates" plus "there are two right answers and the examiner gets to decide which of them is right and change their mind if you pick the right one" adds up to "there is no way to pass this thing without the examiner's permission."
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Re: Harvard class fails (1964) Literacy Test
Jaepheth: You marked 23 as "ok", but I would say that is another one of the misleading questions. It is referring to cardinal directions with reference to a square you draw on the paper in order to correctly answer the question. Is the "northeast corner" of the square the upper right corner or the one that is actually facing to the northeast when you are sitting down to take the test? That's another question that is incredibly easy to grade incorrectly if you are choosing to be malevolent.
Also, you have to realize that people given the test have to complete it all in under 10 minutes, unprepared and out of the blue, with 100% accuracy. You are focusing too much on dissecting individual questions, when the whole point is that it is written opaquely enough that it is difficult to do quickly and under pressure while retaining accuracy.
I'm not understanding why you seem to find the idea so far-fetched, even if we ignore the fact that this is documented historically as being the case. For example, question 3, cross out the longest word in this line. Yes, logically, you would choose the word "longest", since you are looking at the line as a whole. But if you are "grading" it and intentionally setting out to make sure the person who took the test isn't going to pass, it is very easy to say that the question meant what is the longest word in the phrase "this line". Have you never come across that type of trap before in riddles/puzzles and such? It's a really super common way to trick people, by presenting a phrase that can be literally interpreted in multiple ways but "seems" like it should be interpreted in one way based on common speech patterns. It doesn't take a whole lot of brain power on that.That's the thing though. In order to interpret these in any way other than what is obvious you have to deviate so much from both logic, sanity and the spirit of the english language that I do not believe it could be done by some undereducated racist asshat.
Also, you have to realize that people given the test have to complete it all in under 10 minutes, unprepared and out of the blue, with 100% accuracy. You are focusing too much on dissecting individual questions, when the whole point is that it is written opaquely enough that it is difficult to do quickly and under pressure while retaining accuracy.
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Re: Harvard class fails (1964) Literacy Test
Another trap here that I noticed after looking over the questions several times:
Question 7 asks you to put a small cross above the X. A vindictive grader could assess that anything written above that line is part of the answer to the previous questions, allowing them to mark both 6 and 7 as incorrect. They'd mark it that the person taking the test drew three circles and a cross when they were supposed to only draw the 3 circles, and left question 7 blank.
Question 7 asks you to put a small cross above the X. A vindictive grader could assess that anything written above that line is part of the answer to the previous questions, allowing them to mark both 6 and 7 as incorrect. They'd mark it that the person taking the test drew three circles and a cross when they were supposed to only draw the 3 circles, and left question 7 blank.
Re: Harvard class fails (1964) Literacy Test
Also, what do they mean by "Cross"? Do they mean a literal Christian-style cross or an "X" which is also a form of a cross?Civil War Man wrote:Another trap here that I noticed after looking over the questions several times:
Question 7 asks you to put a small cross above the X. A vindictive grader could assess that anything written above that line is part of the answer to the previous questions, allowing them to mark both 6 and 7 as incorrect. They'd mark it that the person taking the test drew three circles and a cross when they were supposed to only draw the 3 circles, and left question 7 blank.
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Re: Harvard class fails (1964) Literacy Test
No one noticed 2 simplest, most obvious things? Curve =/= line, line is straight by definition. You can't wrap it around something. Also, test demands you 'print' not 'write'.
By the way, Jaepheth, you said 21 is ok. But what is correct order? The upside down one or the natural one? You can easily accept either depending if you want one or two axis mirror of the word.
By the way, Jaepheth, you said 21 is ok. But what is correct order? The upside down one or the natural one? You can easily accept either depending if you want one or two axis mirror of the word.
Trivial, just bend local space into continuous curvature. Say, a black hole might helpBorgholio wrote:Um, what? How do you draw a line around anything? It's called a circle...
First word beginning with "L". Meaning, "last". But can also be "literacy" I guessWhat the hell?In the first circle below write the last letter of the first word beginning with "L"
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Re: Harvard class fails (1964) Literacy Test
Are you sure? This is the first time I have heard of that.Irbis wrote:No one noticed 2 simplest, most obvious things? Curve =/= line, line is straight by definition.
A quick search on the net seems to agree with me:
That is why we have to specifically use the term "straight line" when talking about a straight line.http://www.merriam-webster.com/dictionary/line wrote:a straight or curved geometric element that is generated by a moving point and that has extension only along the path of the point
It has become clear to me in the previous days that any attempts at reconciliation and explanation with the community here has failed. I have tried my best. I really have. I pored my heart out trying. But it was all for nothing.
You win. There, I have said it.
Now there is only one thing left to do. Let us see if I can sum up the strength needed to end things once and for all.
You win. There, I have said it.
Now there is only one thing left to do. Let us see if I can sum up the strength needed to end things once and for all.
Re: Harvard class fails (1964) Literacy Test
Per Euclid:
Definition 1.
A point is that which has no part.
Definition 2.
A line is breadthless length.
Definition 3.
The ends of a line are points.
Definition 4.
A straight line is a line which lies evenly with the points on itself.
Definition 5.
A surface is that which has length and breadth only.
Definition 6.
The edges of a surface are lines.
Definition 1.
A point is that which has no part.
Definition 2.
A line is breadthless length.
Definition 3.
The ends of a line are points.
Definition 4.
A straight line is a line which lies evenly with the points on itself.
Definition 5.
A surface is that which has length and breadth only.
Definition 6.
The edges of a surface are lines.
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Re: Harvard class fails (1964) Literacy Test
Thanks JT.
Thus a curve clearly qualifies as a line.
Notice how it being strait is not a requirement. Just that the thing has no breadth, as in no width.JLTucker wrote:Definition 2.
A line is breadthless length.
Notice separate definition for strait line which adds a further qualifier.Definition 4.
A straight line is a line which lies evenly with the points on itself.
Thus a curve clearly qualifies as a line.
It has become clear to me in the previous days that any attempts at reconciliation and explanation with the community here has failed. I have tried my best. I really have. I pored my heart out trying. But it was all for nothing.
You win. There, I have said it.
Now there is only one thing left to do. Let us see if I can sum up the strength needed to end things once and for all.
You win. There, I have said it.
Now there is only one thing left to do. Let us see if I can sum up the strength needed to end things once and for all.
Re: Harvard class fails (1964) Literacy Test
Nope. Unless you classify all rectangles as squares, the same relationship applies:Purple wrote:Thus a curve clearly qualifies as a line.
Line is special case of curve with, as you quoted "which lies evenly with the points on itself". "Straight line" is colloquial, old and incorrect English, at least in my linguistic reference book. I even went and checked my old Analytic Math textbook, says the same, line is special example of curve neither convex nor concave in any point.http://www.encyclopediaofmath.org/index.php/Line_%28curve%29 wrote:A curve in a plane is defined as a set of points whose coordinates satisfy an equation. Restrictions must be imposed on the function so that, on the one hand, the equation should have an infinite set of solutions and, on the other hand, so that this set of solutions does not fill "a piece of the plane".
An important class of curves comprises those for which the function is a polynomial in the two variables; in this case the curve defined by the equation is said to be algebraic. Algebraic curves specified by an equation of the first degree are straight lines. An equation of the second degree that has an infinite set of solutions defines an ellipse, a hyperbola, a parabola, or a curve that splits into two straight lines (which may coincide).