Harvard 1869 entrance exam

http://spectrum.columbiaspectator.com/wp-content/uploads/2011/04/harvardexam.pdf

by alapshah • 15 years ago

169 133 15 years ago

spectrum.columbiaspectator.com

tmsh2• 15 years 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

gbak• 15 years 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...

tmsh2• 15 years 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• 15 years ago

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

leak• 15 years ago

To be fair, you didn't study! Go study man!

dhughes• 15 years 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• 15 years ago

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

derleth4• 15 years ago

Only because it demands regurgitation of specific facts you don't happen to have memorized.

dhconnelly3• 15 years ago

That isn't true. Only the history/geography was recall. Latin translation and geometric proofs aren't regurgitation.

lbarrow• 15 years ago

There were only one or two questions in the mathematical part of the test that I would consider regurgitation -- the rest is stuff modern students should be able to do.

gzavitz• 15 years ago

The students who went to Harvard most likely attended a prep school that taught them for the test.

ry0ohki• 15 years ago

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

barrkel2• 15 years 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• 15 years 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.

dexy• 15 years 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...

32ftpersecond2• 15 years ago

But we've strayed away from the old knowledge (e.g. classics) -- the stuff that keeps repeating itself...

CamperBob• 15 years ago

If history repeats itself, then why not study newer, more relevant iterations?

derleth4• 15 years 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.

twelvechairs2• 15 years 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• 15 years 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.

estevez3• 15 years ago

Plus ça change. There are no such sections in modern standardized admissions tests either.

cad• 15 years 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...) in Turkey may be the best matches for their work positions, but only in 1860s.

orionhickman2• 15 years 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.

dhconnelly3• 15 years 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• 15 years 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.

rdouble• 15 years ago

The SAT math questions are easier than these.

pflats4• 15 years 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.

willyt2• 15 years ago

What age are Americans typically when they take SATS? The geometry stuff is not so bad if you can give visual proofs, pretty hellish otherwise. I think I had to know quite a lot of this stuff for A-level maths as well as Calculus, basic Statistics, Linear Algebra and Applied Maths. But we take these exams when we are 17 and it was 1 of 3 subjects we specialised in for 2 years. Also, regarding your point about calculators, our exam questions were set so that it generally wasn't practical to use a calculator to solve them. E.g. some questions specifically stated that you should give the answer as surd or fraction, it was generally easier / quicker to do the working out manually.

orionhickman2• 15 years ago

It takes a lot of time, but the calculation was definitely something I had to do in elementary school.

In terms of proofs, they are pretty basic, and I learned that stuff in third grade. I mean, I went in and out of gifted programs, but I think the better question is how long does it take to get people to add integers correctly? Ten years?

I drove myself a lot as a child, and drove enough teachers crazy to have to switch schools about ten times before middle school, but I would be surprised if my experience is no longer strictly atypical for people seeking a world-class education.

Note: I didn't attend an Ivy-League, but I did end up skipping a few grades. All those were after elementary school, so it's likely I was ahead of students at the time -- ahead of average, not ahead of the expectations we should have for first class minds seeking a higher education in an age when this is exceptionally uncommon.

balloot• 15 years ago

This math is much harder than the math on the current SAT test. There are no geometry proofs or trig/logarithms on the SAT. However, most admits into Harvard nowadays have either a solid AP Test score in Calculus and/or a SAT2 Math score, so that's sort of an unfair comparison.

michaeldhopkins2• 15 years ago

I've seen this response to the document before and it often turns out the author of the response had missed a page so mistakenly thought there was little math.

There are communities of people who would indeed consider this an easy test but they tend to delve even more deeply into classics than a typical contemporary of the test.

CountHackulus• 15 years 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• 15 years 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.

pflats4• 15 years 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.

jerf3• 15 years 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

mortenjorck• 15 years 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• 15 years 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• 15 years ago

Dante wrote in (what we now call) Italian.

learc83• 15 years 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.

jerf3• 15 years 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.

baddox7• 15 years ago

I think Latin was just a big part of the "culture of the educated." Sure, they could read Latin literature, but they could easily just translate those into English and study English grammar and vocabulary.

baby7• 15 years ago

I don't agree with you. I did 2 years of latin and one year of greek. I don't feel like it really helped me. I actually found it pretty useless except the syntax/grammar part which can be good to understand new languages easier.

It's exactly like learning scheme. Seriously who fucking cares about scheme?

I see latin and greek in a Harvard test as a part of distinguishing highly educated kids from the others.

BrandonM2• 15 years ago

> It's exactly like learning scheme. Seriously who fucking cares about scheme?

Err... This website is written in Arc (a cousin of Scheme), which itself is implemented in MzScheme. So by extension, you care about scheme, and so does everyone else here.

wvoq• 15 years ago

I care about scheme.

c4m• 15 years ago

> It's exactly like learning scheme. Seriously who fucking cares about scheme?

I'm a CS student at the University of Waterloo, where most early CS courses and many advanced courses here use scheme. There are thousands of students taking CS courses here so in fact there is a generation of grads being produced where a significant number (thousands at least) of them base much of their CS knowledge on scheme. That makes it very relevant.

kevinpet• 15 years ago

The point of learning Scheme is that you can learn Scheme the language in five minutes and move on the actual topic of the course, which is about how a program gets executed.

kahawe• 15 years ago

My native tongue is German, I had English as my first and French as my second foreign language and also had quite a few years of Latin in school and I am dabbling in Asian languages just for myself.

I can see how Latin will probably not help with English much (and with French I couldn't see it either) but in comparison German has a LOT more grammatical possibilities and rules and they are very much like Latin except for maybe 2 cases and a few other Latin oddities. This probably makes German comparatively harder for a native English speaker..

The way we had to study Latin was very analytical, never like a spoken language but like dissecting word by word until you could finally understand the sentence. So through studying Latin vocabulary and grammar like that, you got a different and actually excellent insight into your own German mother tongue. And a lot of words, vocabulary and expressions (also in English) at least have Latin (if not Greek) roots.

Some university degrees used to require you to have had Latin in school, medicine was one of those.

The more interesting part of Latin, however, is reading all the great writers and learning about the times they lived in. In a modern Latin class, this should get much more emphasis, even if it happens at the expense of pure language analytical skills.

estevez3• 15 years ago

You might also consider the role that Latin played as the lingua franca of scholarship.

FelixH• 15 years ago

How is Latin the 'source code' of English? Sure, a large number of Latin derived words made it into English (mostly via Norman French), but that's only half the picture

gnu8• 15 years ago

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

impendia4• 15 years 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• 15 years ago

Who here can come up with the most concise explanation?

cousin_it2• 15 years 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)

baby7• 15 years ago

(a^n) * (a^m)

  =

  (a*a*a*a*a) * (a*a*a*a*a*a*a)

      ^              ^

   n times        m times

I don't see what is simpler than this, It comes from the basic definition of what a power is.

twelvechairs2• 15 years ago

The process of explanation by example (though I agree with others that it is really intrinsic in the meaning of a power - id like to hear impendia's explanation):

a^(n+1)=a^n * a

a^(n+2)=a^n * a^2

a^(n+3)=a^n * a^3

a^(n+0)=a^n * a^0

therefore

a^(n+m)=a^n * a^m

lolcraft• 15 years ago

Another "proof":

x^n = exp((log x)n). By definition, exp(n+m)=exp(n)exp(m). By definition, a(b+c) = ab + ac (for the log x thing). QED.

By the way, (the infamous calculus book) Baby Rudin has the poor reader show this property holds in exponentiation for reals, starting with integers and via rationals, as an exercise on its first chapter. Insane difficulty for me, even though the author practically holds your hand along the way! Cool read, though.

fuzionmonkey• 15 years ago

Do you actually find college students that don't know what an exponent is?

I feel like anybody with a basic understanding of what an exponent represents should be able to explain why you add exponents.

impendia4• 15 years ago

They have a working knowledge of it, with very rare exceptions -- but I find that students are taught math as a bunch of rules and not all of them are comfortable giving explanations.

baddox7• 15 years ago

That question stood out to me as a particularly bad question. What is the answer supposed to be? I completely understand how multiplication of exponents works, but I have no idea how to describe the "reason." You can give a simple algebraic proof quite easily (especially if we're just dealing with integer exponents), but unless "reason" had a more specific mathematical meaning in that time, it seems like a very vague question to me.

michaeldhopkins2• 15 years ago

That's the point -- you don't understand it well enough to explain it.

jamieb• 15 years ago

jamieb "google that for you service" (TM):

http://dictionary.reference.com/browse/reason

1. a basis or cause, as for some belief, action, fact, event, etc. ...

3. the mental powers concerned with forming conclusions, judgments, or inferences.

So, its the difference between "reasoning", which we do in math and logic all the time, and "belief" or "motive". That is "reason" did indeed have a specific mathematical meaning at that time, and it still does today.

One might also google "mathematical reasoning"...

tedunangst• 15 years ago

Original source, complete with context and commentary: http://thechoice.blogs.nytimes.com/2011/03/31/remembering-wh...

seagaia• 15 years 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• 15 years 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.

estevez3• 15 years 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• 15 years ago

The source of the Amazon: Seattle?

pak2• 15 years 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• 15 years 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• 15 years ago

I found the handwritten section quite illegible.

bm98• 15 years 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://bm98.posterous.com/did-they-have-latex-in-1869

yvdriess• 15 years ago

Out of curiosity, how did they typeset those mathematical formulae? Still by carefully tiling little metal blocks or with something more advanced.

pak2• 15 years 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-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-f...

abcd_f• 15 years 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• 15 years 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• 15 years ago

Previous discussions

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

http://www.reddit.com/r/reddit.com/comments/glws2/

josscrowcroft• 15 years 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• 15 years 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• 15 years 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.

Harvard 1869 entrance exam

Related Stories