11 ms·

Harvard 1869 entrance exam

169 points by alapshah 15y ago

tmsh 15y ago
Curious to hear about the 'General Supposition' (in the Greek question for sophomores). Seems like it's really only found in New Testament Greek. Makes the test rather biased towards a particular religion. But perhaps that started to change right around that time with Eliot. Charles W. Eliot, president 1869–1909, eliminated the favored position of Christianity from the curriculum while opening it to student self-direction. http://en.wikipedia.org/wiki/Harvard_University http://en.wikipedia.org/wiki/Harvard_University
- gbak 15y ago
  I am Greek and had to do six years of Ancient Greek. I don't understand how you got to that conclusion. The test is asking questions on ancient Greek grammar and only. It has nothing to do with religion or what so ever, New Testament Greek is very close but also very different from Ancient Greek -it has some idiosyncrasies of it's own. I really want to know how you concluded that this has something to do with religion...
  - deleted 15y ago
    [deleted]
  - tmsh 15y ago
    You're right. I spoke too quickly. Thanks. I studied ancient Greek too for several years. I hadn't heard of this 'General Supposition' as a way to describe conditional clauses. Apparently -- just looked it up some -- it was an older way of describing the categories we use now (which are mostly temporal based -- future less-vivid, etc.). So there are two spheres for classifying conditional clauses. If you look up the Goodwin grammar reference for 'General Suppositions', the vast majority are from NT Greek. So that's what made think it was mostly used in NT Greek. So in a way, thinking about conditionals as 'General Suppositions' is sort of biased in that direction. But you're right, could apply to Classical Greek too. I should've remembered that Classical Greek is mostly a superset of NT Greek, so there would be examples there too, etc. But it's actually a rather deep question. Classifying conditions as 'general' asks for a kind of aphoristic understanding of things (talking only about the very general case). I would hazard a guess that the majority of this is in NT Greek. But I suppose some historians and philosophers also generalized (Thucydides, Plato) in this way and could have their protases classified as such. But it is sort of a different way of thinking. Bad to generalize ;-) -- but it may go quite to the heart of certain differences between aspects of NT and ancient Greek.
kellyreid 15y ago
It seems that, neither then nor now, would I have been accepted to Harvard.
- leak 15y ago
  To be fair, you didn't study! Go study man!
- dhughes 15y ago
  Worse than that is this test would have been taken by a person (probably male) straight out of high school. I can't even comprehend what is being asked on most of these questions let alone what it's about, at least if I knew what they were asking I'd be halfway there.
mcweaksauce 15y ago
This looks way harder than the SATs, or rather any standardized test for college admissions that's in use today.
- derleth 15y ago
  Only because it demands regurgitation of specific facts you don't happen to have memorized.
  - dhconnelly 15y ago
    That isn't true. Only the history/geography was recall. Latin translation and geometric proofs aren't regurgitation.
    - veyron 15y ago
      Plane geometry is woefully lacking in education nowadays. The situation is so sad that some of these questions are very similar to the geometry questions in the USAMO/IMO
      - derleth 15y ago
        Plane geometry was, at the time, perhaps the premier formal system to be studied as such; now, we get the same concepts across using calculus (which doesn't seem to be mentioned on the exam) and set theory (which would only really take shape in the 1870s). (The history of mathematics doesn't get so much as a mention, either, but I don't expect it to.)
        jules 15y ago
        This is an interesting "book" that reduces geometry to automated symbol pushing. http://www.math.rutgers.edu/~zeilberg/GT.html http://www.math.rutgers.edu/~zeilberg/GT.html
    - xymostech 15y ago
      Actually from a cursory look at the Latin part, it seemed that all of the sentences and things they chose for you to translate were very specific cases of applying rules. Maybe a bit harder than some of the other stuff, but still regurgitation.
ry0ohki 15y ago
The Latin and Greek parts aside, even the Geography portion is quite difficult, and I have a degree in Geography.
- barrkel 15y ago
  I don't think any of that is difficult; it is, rather, a test of memorization, not ability. A lot of the mathematics section is also on the basis of memorization.
  - wolf550e 15y ago
    In those days, being an educated person meant memorizing a lot of things, because you couldn't haul your library with you everywhere you went, and in any case it didn't have full text search. Separate a modern educated person from google/wikipedia/etc. and see whether they can still converse at the same lavel. Most can't.
    - ricree 15y ago
      There was also a heavy emphasis on a particular subset of history that made up "classical" studies. Besides the river questions, the history and geography questions were about ancient Greece and Rome. There was nothing, for example, on medieval or renaissance history. I suspect that a comparable modern student would have a broader understanding of ancient history than what was shown on this test.
      - SiVal 15y ago
        I suspect not. A comparable modern student would have been exposed to a broader range of ancient history which would also have been shallower and, having been encouraged to "understand" instead of memorizing any of it, would later be left with no real knowledge of anything specific, therefore no real understanding.
    - TeMPOraL 15y ago
      > Separate a modern educated person from google/wikipedia/etc. and see whether they can still converse at the same lavel. Most can't. Relevant xkcd: http://xkcd.com/903/ http://xkcd.com/903/
dexy 15y ago
Amazing how curriculum focus has changed--in no small part due to the invention of the computer. These topics have almost nothing to do with what most Harvard students study today. There's been so much new knowledge generated since then...
- 32ftpersecond 15y ago
  But we've strayed away from the old knowledge (e.g. classics) -- the stuff that keeps repeating itself...
  - CamperBob 15y ago
    If history repeats itself, then why not study newer, more relevant iterations?
    - 32ftpersecond 15y ago
      The Classics are timeless and thus always relevant, that's why they're still read today. Can anyone really argue that reading Jimmy Carter over Cicero or Marcus Aurelius is preferable because of temporal relevancy factors?
derleth 15y ago
Where is the modern history? Where are the questions on governments? Worse, this test doesn't call for much analysis; it's mainly regurgitation of memorized trivia and the most mechanical arithmetical techniques.
- twelvechairs 15y ago
  I agree, but sadly I think a lot of testing is the same now. We are still strongly skewed towards giving people who have rote learned the right things a 'leg up', rather than those with true 'ability'. To be fair though, at least now you can rote learn the right things to pass the tests in any country, not just a few wealthy western schools that teach latin and greek....
  - smspence 15y ago
    I have to completely disagree with this. I think in modern education, it is understood that problem solving and analysis, and being able to learn something and then immediately apply that new knowledge to a different problem, is seen as the most important tool for students today. And I believe that most schools emphasize this today. I found this to be true when I was in high school, college, and also grad school. I also have a very close friend who is now an elementary school teacher (4th grade), and says this as well (they don't just teach with rote memorization). Recently, she was telling me about the subjects she was teaching and the different learning tools they were employing in the class room, and we were having a discussion about how great it was that they are focusing on problem solving and knowledge discovery and not just on rote memorization.
- estevez 15y ago
  Plus ça change. There are no such sections in modern standardized admissions tests either.
cad 15y ago
Same shit happens in Turkey every year. Even the form of the questions are identical. In a sense, people who pass Student Selection and Placement Examination(http://en.wikipedia.org/wiki/Student_Selection_and_Placement_System http://en.wikipedia.org/wiki/Student_Selection_and_Placement...) in Turkey may be the best matches for their work positions, but only in 1860s.
orionhickman 15y ago
The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.
- dhconnelly 15y ago
  I very much doubt that most college students today, even in technical majors, could work out the geometry proofs. I was a calculus TA for two years in college (at an engineering school), and students don't know geometry anymore. Nor can they prove anything at all.
  - BlackJack 15y ago
    Not sure why this is, or was, getting downvoted. For most high school students, geometry consists of 1 semester in their entire high school career, and it mostly involves learning about triangles and polygons and learning the (n-2)/180 formula and a few, trivial proofs. The depth of Geometry on the Harvard test is not very deep per se, but it's easily out of reach for most high schoolers. Now the students who do math contests and are AIME/USAMO level could probably do the geometry section here without a lot of trouble, but they are the exception.
    - pflats 15y ago
      If things continue as they are, expect this to change a bit. In particular, proofs like #4 on Geometry is going to be a requirement in 45 of the 50 states. Check G-SRT.4 at http://www.corestandards.org/the-standards/mathematics/high-school-geometry/similarity-right-triangles-and-trigonometry/ http://www.corestandards.org/the-standards/mathematics/high-...
- rdouble 15y ago
  The SAT math questions are easier than these.
- pflats 15y ago
  You're exaggerating more than a little bit. There's 2 trigonometric proofs, and a number of less than obvious geometric proofs, especially the latter ones pertaining to the circle. The rational equation in #8 on algebra going to involve solving a cubic. And although #7 in arithmetic wouldn't be too hard if you worked entirely in pence, it is still a trickier problem in the days before decimalization. Granted, it's weird in this day of students taking 5+ AP classes to see no calculus, but the math isn't weak at all. Remember, there's no calculators here. Maybe a slide rule and a table of trig values/logarithms. But that's still a lot of work by hand.
CountHackulus 15y ago
I'm surprised there's no calculus. Not even a basic derivative. The rest of the exam is certainly difficult to warrant a calculus question.
- william42 15y ago
  I think that at that point calculus was a grad-school-level thing. At the very least, it wasn't being taught in high schools. In fact, I'm pretty sure it's only taught in high schools today under the aegis of Advanced Placement classes, which give you college credit.
  - pflats 15y ago
    Many, many schools today offer "College Prep" calculus, which is far less rigorous than AP Calc. It covers most of the same topics, but with less depth. It's unlikely a College Prep Calc class would spend much time, if any, memorizing Trig Identities for integration. Generally very little epsilon-delta work, etc.
    - dan-k 15y ago
      I'd be surprised if they do more than mention that epsilon-delta stuff exists. Most AP calc classes have very little epsilon-delta work. We spent maybe two or three days on it in mine, certainly not enough time to write a full proof, and that was more than most people I've talked to who did it at different high schools. If my experience is at all representative, that rigorous of a development of calculus isn't normal until upper-level classes, when you're heading towards analysis.
- jerf 15y ago
  While Calculus may nominally have been invented a couple of centuries earlier, even by 1869 it still had a lot of development to go through before it would approach the relative ease of modern calculus. Limits were still only a few decades old, with the modern notation for it not developed until 1908[1]. It takes a long time for things to go from the cutting edge of math down to pre-college curricula. Perhaps some students had been exposed to it, but testing for it on the entrance exam may not have provided much information for the examiners. In fact, reading that sort of makes me curious about what pedagogical approach was taken to teach pre-limit calculus. [1]: http://en.wikipedia.org/wiki/Limit_of_a_function http://en.wikipedia.org/wiki/Limit_of_a_function
mortenjorck 15y ago
In a way, this reinforces my hypothesis that Latin in traditional Western higher education was never quite so much about Latin itself as it was about gaining a deeper understanding and greater praxis of your native tongue by reading its source code.
- boredguy8 15y ago
  Uhm, what? You couldn't be more off. Traditionally, any liberal arts education would include extensive familiarity with the classics. That means Plato & Dante, at the minimum, whether a BA or BS. You were expected to know Latin and Greek because you were expected to read Latin and Greek. If you were pursuing a BS, then perhaps you would read Euclid's "Elements" instead of Thucydides' "The History of the Peloponnesian War". (&c., It's not like those were the only texts one would encounter.) But languages were a prerequisite because they lacked the chronological hubris of our age. Hence the tight coupling with Geography: notice the ties between Xenophon in translation & the role of the Ten Thousand in Geography.
  - jacobolus 15y ago
    Dante wrote in (what we now call) Italian.
    - DrJokepu 15y ago
      My understanding is that even for native Italians it's very difficult to understand Dante as it's rather archaic. I'm not sure that being able to read Latin would be of any help.
  - learc83 15y ago
    I think it was also a bit of holdover from a previous time, when Latin and Greek texts represented the pinnacle of human knowledge.
  - jerf 15y ago
    It isn't "chronological hubris" that the vast bulk of human knowledge has been generated since 1869. Precise measurement is difficult to even define but it's difficult to imagine a non-pathological definition for which that would not be true. Personally I'm a huge advocate for the fact that what one might call "wisdom" is not unique to our age and may indeed be getting a bit lost in the shuffle, but nevertheless, there's no way that we can go back to covering everything that took 12 years to learn in 1869 and cover all the things that take 12 years to learn today. When you push an hour into the curriculum to cover, say, the basic functioning of electricity, to name just one thing that I think one should not be able to escape from modern schooling without having gotten exposed to at some point, an hour has to come out of it somewhere else.
gnu8 15y ago
http://news.ycombinator.com/item?id=2426655 http://news.ycombinator.com/item?id=2426655
impendia 15y ago
> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
- hammock 15y ago
  Who here can come up with the most concise explanation?
  - cousin_it 15y ago
    Me, me! Let me try! X^N * X^M = N copies of X, multiplied by M copies of X = N+M copies of X multiplied together = X^(N+M)
    - baddox 15y ago
      That's not very rigorous, especially with fractional (or God forbid, irrational) exponents.
      - cousin_it 15y ago
        Yeah, and I'd be even more interested in a similarly intuitive explanation for the case of complex exponents ;-)
        baddox 15y ago
        That would be difficult, since a formal construction of even the real numbers is a somewhat advanced (3rd or 4th year college mathematics) topic. I forget the details, but I believe a^n for real a and complex n is formally defined using the exponential function (e^x).
        15y ago
tedunangst 15y ago
Original source, complete with context and commentary: http://thechoice.blogs.nytimes.com/2011/03/31/remembering-when-college-was-a-buyers-bazaar/ http://thechoice.blogs.nytimes.com/2011/03/31/remembering-wh...
seagaia 15y ago
does the requirement of Latin strike anyone as a bit elitist? or was Latin really that necessary in order to (presumably) study some Classics?
- dpe82 15y ago
  The European university tradition on which Harvard was created treated Latin and Greek as the languages of learning. At the time a college education included a rigorous treatment of the classics (Latin) and philosophy (Greek). The belief was probably that they couldn't be truly appreciated understood unless studied in the original language (which is arguably true). And of practical note, some scientific writing was still done in Latin at the time and the language was still in wide use in throughout Europe. Heck, I learned Latin in high school in the late 90s. I hated it when I took it, but it certainly made learning other things a lot easier.
- estevez 15y ago
  College education was intended for the elite. The proportion of the population that possessed a high school diploma, much less a college degree was infinitesimal. Indeed, as late as the 1950s, only ~8% of the population were college graduates. In practice, the requirement for the classics was no impediment to elites; one could be admitted on the condition that shortcomings would be remediated. Once admitted, you could easily purchase the services of a tutor or cheat your way through.
mmaunder 15y ago
The source of the Amazon: Seattle?
pak 15y ago
The thing I noticed (sorry, LaTeX fan here) was how well they could typeset math and Latin all the way back in 1869! I have to say I'm impressed, and it makes me a bit sad that most of my college exams looked worse (typographically) than a paper produced over a century ago. Look at those goddamn gorgeously even margins, the ligatures, the kerning of the italics, and the protrusion of the hyphens. Hell, this makes the SATs, with its ragged edges and sloppy Times New Roman straight out of MS Word, look like carelessly produced junk.
- kijin 15y ago
  It's also interesting that the Greek portion of the exam was handwritten. Perhaps Harvard University Press didn't have movable types for Greek letters at that time? Also, I'm curious how they distributed the handwritten pages to all the applicants (hundreds?) without a Xerox machine.
  - bowyakka 15y ago
    I found the handwritten section quite illegible.
- bm98 15y ago
  An 1869 MIT entrance exam was posted here a while back and the typesetting was similar: http://news.ycombinator.com/item?id=1967040 http://news.ycombinator.com/item?id=1967040 http://bm98.posterous.com/did-they-have-latex-in-1869 http://bm98.posterous.com/did-they-have-latex-in-1869
- yvdriess 15y ago
  Out of curiosity, how did they typeset those mathematical formulae? Still by carefully tiling little metal blocks or with something more advanced.
  - pak 15y ago
    I was wondering this myself. I think that they were still tiling little metal blocks, according to this picture: http://www.datadeluge.com/2010/09/how-maths-was-typeset-before-latex.html http://www.datadeluge.com/2010/09/how-maths-was-typeset-befo... Which makes it all the more impressive--each page took considerable craft and attention to detail. For more information on this, you'd have to get a book like this one--I can't find anything more online: http://www.worldcat.org/title/printing-of-mathematics-aids-for-authors-and-editors-and-rules-for-compositors-and-readers-at-the-university-press-oxford/oclc/220341904 http://www.worldcat.org/title/printing-of-mathematics-aids-f...
abcd_f 15y ago
> Find cube root of 0.0093 to five places of decimals Nice, reminds me of > Find 7th root of 0.9999 to four places of decimals :)
- gjm11 15y ago
  The latter is much much easier: the answer is 1.0000, and "obviously" so. Now, if you happen to know that 21^3=9261 then you can do the 0.0093 one to 5dp with only a few lines of calculation, but it's distinctly more work than the 0.9999 one even so.
est 15y ago
Previous discussions http://news.ycombinator.com/item?id=2426655 http://news.ycombinator.com/item?id=2426655 http://www.reddit.com/r/reddit.com/comments/glws2/ http://www.reddit.com/r/reddit.com/comments/glws2/
josscrowcroft 15y ago
I would love to read a blog post where somebody answers all of these to a high enough standard to be admitted in 1869!
samsol 15y ago
The good thing about entrance (seemingly thought-provoking) exams is that , they used to concentrate on the real sciences/ social sciences . And used to test aptitude in these disciplines to ensure that people who pursue them have enough passion to go thru end. And they let leadership skills emerge after acquiring those analytical/ philosophical skills. Rather than in the current education system where very very few people want to proceed working in these pure sciences and majority of them want to become leaders and thanks to Univs of US in which leaders are "annointed" by dishing out MBA's based on GMAT / CAT scores.
mixmastamyk 15y ago
Looks pretty tough... I haven't studied many of these subjects seriously in years. I think its safe to say a high-acheiving school board member[1] would fail handily. [1] See today's links.

169 points by alapshah 15y ago

tmsh 15y ago

Curious to hear about the 'General Supposition' (in the Greek question for sophomores). Seems like it's really only found in New Testament Greek. Makes the test rather biased towards a particular religion. But perhaps that started to change right around that time with Eliot. Charles W. Eliot, president 1869–1909, eliminated the favored position of Christianity from the curriculum while opening it to student self-direction. http://en.wikipedia.org/wiki/Harvard_University http://en.wikipedia.org/wiki/Harvard_University

gbak 15y ago
I am Greek and had to do six years of Ancient Greek. I don't understand how you got to that conclusion. The test is asking questions on ancient Greek grammar and only. It has nothing to do with religion or what so ever, New Testament Greek is very close but also very different from Ancient Greek -it has some idiosyncrasies of it's own. I really want to know how you concluded that this has something to do with religion...
- deleted 15y ago
  [deleted]
- tmsh 15y ago
  You're right. I spoke too quickly. Thanks. I studied ancient Greek too for several years. I hadn't heard of this 'General Supposition' as a way to describe conditional clauses. Apparently -- just looked it up some -- it was an older way of describing the categories we use now (which are mostly temporal based -- future less-vivid, etc.). So there are two spheres for classifying conditional clauses. If you look up the Goodwin grammar reference for 'General Suppositions', the vast majority are from NT Greek. So that's what made think it was mostly used in NT Greek. So in a way, thinking about conditionals as 'General Suppositions' is sort of biased in that direction. But you're right, could apply to Classical Greek too. I should've remembered that Classical Greek is mostly a superset of NT Greek, so there would be examples there too, etc. But it's actually a rather deep question. Classifying conditions as 'general' asks for a kind of aphoristic understanding of things (talking only about the very general case). I would hazard a guess that the majority of this is in NT Greek. But I suppose some historians and philosophers also generalized (Thucydides, Plato) in this way and could have their protases classified as such. But it is sort of a different way of thinking. Bad to generalize ;-) -- but it may go quite to the heart of certain differences between aspects of NT and ancient Greek.

kellyreid 15y ago

It seems that, neither then nor now, would I have been accepted to Harvard.

leak 15y ago
To be fair, you didn't study! Go study man!
dhughes 15y ago
Worse than that is this test would have been taken by a person (probably male) straight out of high school. I can't even comprehend what is being asked on most of these questions let alone what it's about, at least if I knew what they were asking I'd be halfway there.

mcweaksauce 15y ago

This looks way harder than the SATs, or rather any standardized test for college admissions that's in use today.

derleth 15y ago
Only because it demands regurgitation of specific facts you don't happen to have memorized.
- dhconnelly 15y ago
  That isn't true. Only the history/geography was recall. Latin translation and geometric proofs aren't regurgitation.
  - veyron 15y ago
    Plane geometry is woefully lacking in education nowadays. The situation is so sad that some of these questions are very similar to the geometry questions in the USAMO/IMO
    - derleth 15y ago
      Plane geometry was, at the time, perhaps the premier formal system to be studied as such; now, we get the same concepts across using calculus (which doesn't seem to be mentioned on the exam) and set theory (which would only really take shape in the 1870s). (The history of mathematics doesn't get so much as a mention, either, but I don't expect it to.)
      - jules 15y ago
        This is an interesting "book" that reduces geometry to automated symbol pushing. http://www.math.rutgers.edu/~zeilberg/GT.html http://www.math.rutgers.edu/~zeilberg/GT.html
  - xymostech 15y ago
    Actually from a cursory look at the Latin part, it seemed that all of the sentences and things they chose for you to translate were very specific cases of applying rules. Maybe a bit harder than some of the other stuff, but still regurgitation.

ry0ohki 15y ago

The Latin and Greek parts aside, even the Geography portion is quite difficult, and I have a degree in Geography.

barrkel 15y ago
I don't think any of that is difficult; it is, rather, a test of memorization, not ability. A lot of the mathematics section is also on the basis of memorization.
- wolf550e 15y ago
  In those days, being an educated person meant memorizing a lot of things, because you couldn't haul your library with you everywhere you went, and in any case it didn't have full text search. Separate a modern educated person from google/wikipedia/etc. and see whether they can still converse at the same lavel. Most can't.
  - ricree 15y ago
    There was also a heavy emphasis on a particular subset of history that made up "classical" studies. Besides the river questions, the history and geography questions were about ancient Greece and Rome. There was nothing, for example, on medieval or renaissance history. I suspect that a comparable modern student would have a broader understanding of ancient history than what was shown on this test.
    - SiVal 15y ago
      I suspect not. A comparable modern student would have been exposed to a broader range of ancient history which would also have been shallower and, having been encouraged to "understand" instead of memorizing any of it, would later be left with no real knowledge of anything specific, therefore no real understanding.
  - TeMPOraL 15y ago
    > Separate a modern educated person from google/wikipedia/etc. and see whether they can still converse at the same lavel. Most can't. Relevant xkcd: http://xkcd.com/903/ http://xkcd.com/903/

dexy 15y ago

Amazing how curriculum focus has changed--in no small part due to the invention of the computer. These topics have almost nothing to do with what most Harvard students study today. There's been so much new knowledge generated since then...

32ftpersecond 15y ago
But we've strayed away from the old knowledge (e.g. classics) -- the stuff that keeps repeating itself...
- CamperBob 15y ago
  If history repeats itself, then why not study newer, more relevant iterations?
  - 32ftpersecond 15y ago
    The Classics are timeless and thus always relevant, that's why they're still read today. Can anyone really argue that reading Jimmy Carter over Cicero or Marcus Aurelius is preferable because of temporal relevancy factors?

derleth 15y ago

Where is the modern history? Where are the questions on governments? Worse, this test doesn't call for much analysis; it's mainly regurgitation of memorized trivia and the most mechanical arithmetical techniques.

twelvechairs 15y ago
I agree, but sadly I think a lot of testing is the same now. We are still strongly skewed towards giving people who have rote learned the right things a 'leg up', rather than those with true 'ability'. To be fair though, at least now you can rote learn the right things to pass the tests in any country, not just a few wealthy western schools that teach latin and greek....
- smspence 15y ago
  I have to completely disagree with this. I think in modern education, it is understood that problem solving and analysis, and being able to learn something and then immediately apply that new knowledge to a different problem, is seen as the most important tool for students today. And I believe that most schools emphasize this today. I found this to be true when I was in high school, college, and also grad school. I also have a very close friend who is now an elementary school teacher (4th grade), and says this as well (they don't just teach with rote memorization). Recently, she was telling me about the subjects she was teaching and the different learning tools they were employing in the class room, and we were having a discussion about how great it was that they are focusing on problem solving and knowledge discovery and not just on rote memorization.
estevez 15y ago
Plus ça change. There are no such sections in modern standardized admissions tests either.

cad 15y ago

Same shit happens in Turkey every year. Even the form of the questions are identical. In a sense, people who pass Student Selection and Placement Examination(http://en.wikipedia.org/wiki/Student_Selection_and_Placement_System http://en.wikipedia.org/wiki/Student_Selection_and_Placement...) in Turkey may be the best matches for their work positions, but only in 1860s.

orionhickman 15y ago

The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.

dhconnelly 15y ago
I very much doubt that most college students today, even in technical majors, could work out the geometry proofs. I was a calculus TA for two years in college (at an engineering school), and students don't know geometry anymore. Nor can they prove anything at all.
- BlackJack 15y ago
  Not sure why this is, or was, getting downvoted. For most high school students, geometry consists of 1 semester in their entire high school career, and it mostly involves learning about triangles and polygons and learning the (n-2)/180 formula and a few, trivial proofs. The depth of Geometry on the Harvard test is not very deep per se, but it's easily out of reach for most high schoolers. Now the students who do math contests and are AIME/USAMO level could probably do the geometry section here without a lot of trouble, but they are the exception.
  - pflats 15y ago
    If things continue as they are, expect this to change a bit. In particular, proofs like #4 on Geometry is going to be a requirement in 45 of the 50 states. Check G-SRT.4 at http://www.corestandards.org/the-standards/mathematics/high-school-geometry/similarity-right-triangles-and-trigonometry/ http://www.corestandards.org/the-standards/mathematics/high-...
rdouble 15y ago
The SAT math questions are easier than these.
pflats 15y ago
You're exaggerating more than a little bit. There's 2 trigonometric proofs, and a number of less than obvious geometric proofs, especially the latter ones pertaining to the circle. The rational equation in #8 on algebra going to involve solving a cubic. And although #7 in arithmetic wouldn't be too hard if you worked entirely in pence, it is still a trickier problem in the days before decimalization. Granted, it's weird in this day of students taking 5+ AP classes to see no calculus, but the math isn't weak at all. Remember, there's no calculators here. Maybe a slide rule and a table of trig values/logarithms. But that's still a lot of work by hand.

CountHackulus 15y ago

I'm surprised there's no calculus. Not even a basic derivative. The rest of the exam is certainly difficult to warrant a calculus question.

william42 15y ago
I think that at that point calculus was a grad-school-level thing. At the very least, it wasn't being taught in high schools. In fact, I'm pretty sure it's only taught in high schools today under the aegis of Advanced Placement classes, which give you college credit.
- pflats 15y ago
  Many, many schools today offer "College Prep" calculus, which is far less rigorous than AP Calc. It covers most of the same topics, but with less depth. It's unlikely a College Prep Calc class would spend much time, if any, memorizing Trig Identities for integration. Generally very little epsilon-delta work, etc.
  - dan-k 15y ago
    I'd be surprised if they do more than mention that epsilon-delta stuff exists. Most AP calc classes have very little epsilon-delta work. We spent maybe two or three days on it in mine, certainly not enough time to write a full proof, and that was more than most people I've talked to who did it at different high schools. If my experience is at all representative, that rigorous of a development of calculus isn't normal until upper-level classes, when you're heading towards analysis.
jerf 15y ago
While Calculus may nominally have been invented a couple of centuries earlier, even by 1869 it still had a lot of development to go through before it would approach the relative ease of modern calculus. Limits were still only a few decades old, with the modern notation for it not developed until 1908[1]. It takes a long time for things to go from the cutting edge of math down to pre-college curricula. Perhaps some students had been exposed to it, but testing for it on the entrance exam may not have provided much information for the examiners. In fact, reading that sort of makes me curious about what pedagogical approach was taken to teach pre-limit calculus. [1]: http://en.wikipedia.org/wiki/Limit_of_a_function http://en.wikipedia.org/wiki/Limit_of_a_function

mortenjorck 15y ago

In a way, this reinforces my hypothesis that Latin in traditional Western higher education was never quite so much about Latin itself as it was about gaining a deeper understanding and greater praxis of your native tongue by reading its source code.

boredguy8 15y ago
Uhm, what? You couldn't be more off. Traditionally, any liberal arts education would include extensive familiarity with the classics. That means Plato & Dante, at the minimum, whether a BA or BS. You were expected to know Latin and Greek because you were expected to read Latin and Greek. If you were pursuing a BS, then perhaps you would read Euclid's "Elements" instead of Thucydides' "The History of the Peloponnesian War". (&c., It's not like those were the only texts one would encounter.) But languages were a prerequisite because they lacked the chronological hubris of our age. Hence the tight coupling with Geography: notice the ties between Xenophon in translation & the role of the Ten Thousand in Geography.
- jacobolus 15y ago
  Dante wrote in (what we now call) Italian.
  - DrJokepu 15y ago
    My understanding is that even for native Italians it's very difficult to understand Dante as it's rather archaic. I'm not sure that being able to read Latin would be of any help.
- learc83 15y ago
  I think it was also a bit of holdover from a previous time, when Latin and Greek texts represented the pinnacle of human knowledge.
- jerf 15y ago
  It isn't "chronological hubris" that the vast bulk of human knowledge has been generated since 1869. Precise measurement is difficult to even define but it's difficult to imagine a non-pathological definition for which that would not be true. Personally I'm a huge advocate for the fact that what one might call "wisdom" is not unique to our age and may indeed be getting a bit lost in the shuffle, but nevertheless, there's no way that we can go back to covering everything that took 12 years to learn in 1869 and cover all the things that take 12 years to learn today. When you push an hour into the curriculum to cover, say, the basic functioning of electricity, to name just one thing that I think one should not be able to escape from modern schooling without having gotten exposed to at some point, an hour has to come out of it somewhere else.

gnu8 15y ago

http://news.ycombinator.com/item?id=2426655 http://news.ycombinator.com/item?id=2426655

impendia 15y ago

> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.

hammock 15y ago
Who here can come up with the most concise explanation?
- cousin_it 15y ago
  Me, me! Let me try! X^N * X^M = N copies of X, multiplied by M copies of X = N+M copies of X multiplied together = X^(N+M)
  - baddox 15y ago
    That's not very rigorous, especially with fractional (or God forbid, irrational) exponents.
    - cousin_it 15y ago
      Yeah, and I'd be even more interested in a similarly intuitive explanation for the case of complex exponents ;-)
      - baddox 15y ago
        That would be difficult, since a formal construction of even the real numbers is a somewhat advanced (3rd or 4th year college mathematics) topic. I forget the details, but I believe a^n for real a and complex n is formally defined using the exponential function (e^x).
        15y ago

tedunangst 15y ago

Original source, complete with context and commentary: http://thechoice.blogs.nytimes.com/2011/03/31/remembering-when-college-was-a-buyers-bazaar/ http://thechoice.blogs.nytimes.com/2011/03/31/remembering-wh...

seagaia 15y ago

does the requirement of Latin strike anyone as a bit elitist? or was Latin really that necessary in order to (presumably) study some Classics?

dpe82 15y ago
The European university tradition on which Harvard was created treated Latin and Greek as the languages of learning. At the time a college education included a rigorous treatment of the classics (Latin) and philosophy (Greek). The belief was probably that they couldn't be truly appreciated understood unless studied in the original language (which is arguably true). And of practical note, some scientific writing was still done in Latin at the time and the language was still in wide use in throughout Europe. Heck, I learned Latin in high school in the late 90s. I hated it when I took it, but it certainly made learning other things a lot easier.
estevez 15y ago
College education was intended for the elite. The proportion of the population that possessed a high school diploma, much less a college degree was infinitesimal. Indeed, as late as the 1950s, only ~8% of the population were college graduates. In practice, the requirement for the classics was no impediment to elites; one could be admitted on the condition that shortcomings would be remediated. Once admitted, you could easily purchase the services of a tutor or cheat your way through.

mmaunder 15y ago

The source of the Amazon: Seattle?

pak 15y ago

The thing I noticed (sorry, LaTeX fan here) was how well they could typeset math and Latin all the way back in 1869! I have to say I'm impressed, and it makes me a bit sad that most of my college exams looked worse (typographically) than a paper produced over a century ago. Look at those goddamn gorgeously even margins, the ligatures, the kerning of the italics, and the protrusion of the hyphens. Hell, this makes the SATs, with its ragged edges and sloppy Times New Roman straight out of MS Word, look like carelessly produced junk.

kijin 15y ago
It's also interesting that the Greek portion of the exam was handwritten. Perhaps Harvard University Press didn't have movable types for Greek letters at that time? Also, I'm curious how they distributed the handwritten pages to all the applicants (hundreds?) without a Xerox machine.
- bowyakka 15y ago
  I found the handwritten section quite illegible.
bm98 15y ago
An 1869 MIT entrance exam was posted here a while back and the typesetting was similar: http://news.ycombinator.com/item?id=1967040 http://news.ycombinator.com/item?id=1967040 http://bm98.posterous.com/did-they-have-latex-in-1869 http://bm98.posterous.com/did-they-have-latex-in-1869
yvdriess 15y ago
Out of curiosity, how did they typeset those mathematical formulae? Still by carefully tiling little metal blocks or with something more advanced.
- pak 15y ago
  I was wondering this myself. I think that they were still tiling little metal blocks, according to this picture: http://www.datadeluge.com/2010/09/how-maths-was-typeset-before-latex.html http://www.datadeluge.com/2010/09/how-maths-was-typeset-befo... Which makes it all the more impressive--each page took considerable craft and attention to detail. For more information on this, you'd have to get a book like this one--I can't find anything more online: http://www.worldcat.org/title/printing-of-mathematics-aids-for-authors-and-editors-and-rules-for-compositors-and-readers-at-the-university-press-oxford/oclc/220341904 http://www.worldcat.org/title/printing-of-mathematics-aids-f...

abcd_f 15y ago

> Find cube root of 0.0093 to five places of decimals Nice, reminds me of > Find 7th root of 0.9999 to four places of decimals :)

gjm11 15y ago
The latter is much much easier: the answer is 1.0000, and "obviously" so. Now, if you happen to know that 21^3=9261 then you can do the 0.0093 one to 5dp with only a few lines of calculation, but it's distinctly more work than the 0.9999 one even so.

est 15y ago

Previous discussions http://news.ycombinator.com/item?id=2426655 http://news.ycombinator.com/item?id=2426655 http://www.reddit.com/r/reddit.com/comments/glws2/ http://www.reddit.com/r/reddit.com/comments/glws2/

josscrowcroft 15y ago

I would love to read a blog post where somebody answers all of these to a high enough standard to be admitted in 1869!

samsol 15y ago

The good thing about entrance (seemingly thought-provoking) exams is that , they used to concentrate on the real sciences/ social sciences . And used to test aptitude in these disciplines to ensure that people who pursue them have enough passion to go thru end. And they let leadership skills emerge after acquiring those analytical/ philosophical skills. Rather than in the current education system where very very few people want to proceed working in these pure sciences and majority of them want to become leaders and thanks to Univs of US in which leaders are "annointed" by dishing out MBA's based on GMAT / CAT scores.

mixmastamyk 15y ago

Looks pretty tough... I haven't studied many of these subjects seriously in years. I think its safe to say a high-acheiving school board member[1] would fail handily. [1] See today's links.