Harvard's 1899 Entrance Exam [pdf] | Hacker News Reader

Harvard's 1899 Entrance Exam [pdf]

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189 pointsbenjaminfox91 comments

Like all tests, it's not hard if you know the stuff that's asked. If you've studied ancient greek in school, that part of the test is probably as easy for you as the algebra part must seem to anyone who went to school in the past couple of decades (it looks about as hard as math homework from when I was 15 or so).

edit:

It's interesting. I do have a certain romantic attachment to this kind of classic humanist education, e.g. it irks me that the history and geography section has me floundered and I'm somewhat sorry that I didn't have the drive to do better in Latin in school.

But then I think, there's so much other interesting things to know and experience. At times when I wish I could read Cicero's Orationes In Catilinam in its original form, I need to remind myself that I can read and understand, say, this little piece of genius:

  fib = 1 : 1 : [ a+b | (a,b) <- zip fib (tail fib) ]

But to become a fully erudite member of modern society, you might want to also study

  zipWith :: (a-> b -> c) -> [a] -> [b] -> [c]

:-)

Allowing one to simplify to:

  fibs = 1 : 1 : zipWith (+) fibs (tail fibs)

Involving zip`ap`tail, the Aztec god of consecutive numbers:

  fibs = 1 : 1 : (zipWith (+) `ap` tail) fibs

Or, pointlessly:

  fix $ (1:) . (1:) . (zipWith (+) `ap` tail)

Your second example does not typecheck.

It does.

let fibs = 1 : 1 : (zipWith (+) `ap` tail) fibs in fibs :: (Num a) => [a]

according to ghci 6.12.1

I get No instance for (Monad ((->) [a])) -am I missing some module include?

What is truly amazing is how easy it is to find those answers today. With Google, Wolframalpha, etc. retrieving information is cheap both time wise and money wise.

Perhaps a test could be made today that would test a person's ability to search for obscure knowledge and comprehend it. A person would have to determine which sources are trustworthy and what conclusion could be made from the information received. Is this what is really meant when we say someone is intelligent?

I think we're moving from single answer knowledge to multi-answer understanding of the matter. This involves being able to absorb large amounts of information, rather than being able to find obscure information. We probably need more knowledge than ever before, but it has more breadth and less specificity.

A historian might be asked to discuss why Spain and Portugal were the first of the European countries to build a colonial empire. You wouldn't directly find that on wikipedia and there is not one single answer that will suffice. To be able to answer it, you need to be aware of the Reconquista, abundant military resources, conquered wealth, etc. and be able to support any claim you make about them. You can search for the details, but you need to have a broad enough knowledge to know what to search for.

A mathematician might be asked about the importance of prime numbers in mathematics. Again, not something on wikipedia, Google, or wolfram alpha, or with a single answer.

This is the essence of what I was getting at. You've elaborated on what I was getting at.

It's somewhat pointless to ask on a test when the U.S. Civil War ended. A much better indication of intelligence and knowledge is to ask why it didn't end sooner.

Not too long ago people would spend hundreds of dollars (thousands in today's money) for a set of encyclopedias. Now, with Google, Wolframalpha etc. such a product has no use. The cost to find knowledge has dramatically decreased the past 15 years. Education has not caught up with this reality.

One of the best examples for an exam like this was the final exam in history at my high school. Half of it was a few class-wide topics of 20th century history. The other half was anything of the students choosing, I've chosen the policy of Perestroika of Gorbatschov and the downfall of the Sowjet Union.

The exam was simply a text snippet (dunno anymore whether newspaper or something more official) from the time about the reunion of the two Germans, and the assignment was to put it into greater context and connect it with other things that happened at the time, hereby explaining this particular incident. The questions for the general part were of similar spirit.

It's been one of the best exams I've ever had. Not just because I've got a straight A, but also because I've actually _learned_ something while writing it: It forced me to think about the knowledge I've already amassed from a different pov for two hours, greatly increasing my understanding of it.

I think every exam should be like that: If you haven't learned anything new while writing/having it, it's likely just pointless rendition of stuff learned by heart. And frankly, computers just beat humans at that ;-). Of course, doing this requires good teachers and quite an investment of time from them.

I found some Cambridge exam papers from 1899 a while back. I don't have scans, but there's a few of the more interesting/mysterious questions at:

http://beebo.org/lately/2001-07-10_cambridge.html

I quite like the 2.5 hour "English Essay" for bizarreness:

Write an English Essay on one of the following subjects:

1. English country life in the 18th century. 2. The battle of Blenheim. 3. The character of Rachel Lady Castlewood. 4. Duelling.

I'm not sure what you find bizarre, having to write an essay or the choice of topics? This type of question is pretty much standard on (high school) English exams in many commonwealth countries, even today.

They have duels in your country?!

No, but they are still a topic in fiction / history.

The choice of topics, really. This was for (I think) an entrance exam, and so the only topic I think even vaguely suitable to write about without forewarning is "English country life in the 18th century." The Battle of Blenheim and the character of Rachel Lady Castlewood can only be attempted if you already know about those (very specific) things, and duelling is broad, and odd.

I don't know whether this is an entrance exam and that would definitely change things.

But either way, according to Wikipedia, dueling was a part of British culture though the early 1800s, the last fatal duel was in 1856. Meaning a typical candidate from an elite family in 1899 will have a living relative who has probably at least read public discourse about dueling, and there's a good chance the subject has come up at least once during primary education.

Scotland's last-ever duel with swords was fought in the same year: 1899.

"Swords were drawn and blood was spilled over the election battle of the University Rector."

It was in a semi-public place (the Glasgow University Union building) and may have been reported at the time. Thus, duelling may have been in the news at the time.

http://www.theguu.com/about/history/

In a bold attempt to prove myself wrong I offer this other link that suggests that the story (well-known to alumni of Glasgow University, such as myself) may have been a fictional, satirical sketch written for the student magazine.

"It found no other mention of the event in contemporary university records, newspapers or court summaries."

http://news.scotsman.com/education/Hit-and-myth-Was-Scotland...

I guess it's loosely equivalent to an essay topic today on:

1. English city life in the 19th century. 2. The Battle of the Somme 3. The character of Lady Chatterley 4. Apartheid

I'd expect that whilst they might seem absurdly dated 100 years from now many contemporary British Cambridge applicants today could confidently write essays on (2), a fair few on (3). I'd be really happy if (4) seemed like an odd subject in 100 years' time.

Until recently, the Oxford All Souls entrance exam had one paper which was a single word that you had to write about for three hours.

I gather that they've dropped it now, I assume because it confirmed for many people that the main thing an Oxford education prepared you for was bullshitting on topics you know nothing about.

(Full disclosure: I went to Oxford)

how do you measure the hours someone used to write something?

i'd have studied decorative calligraphy and spent 2.5 hours on the title.

Presumably you're merely allotted 2.5 hours. How you spend them is up to you, but the resulting essay is graded.

This test shows what was valued - at least at Harvard - in the late 1800's. Greek and Latin were more important, as well as knowledge of geography of the known world and algebra and geometry.

Algebra and geometry, I feel, are still important today (see SAT). Greek and Latin are less important, although they are still in the background. The humanities have changed and we now learn about more modern authors / topics and the humanities classes in general have cooler names (i.e. Microcomputer Application in Kinesiology or Topics in African Society and Culture).

There's probably some bigger point I'm missing here like "those who don't learn from history are doomed to repeat it" or something similar.

Teaching kids about how to conjugate Latin verbs or some other rote activity always seemed pointless to me. Perhaps I'm preaching to the choir, but learning about entrepreneurship or practicing selling things would have been much more useful to me than many of the things I learned in high school or undergrad.

Latin is and most likely already was in the XIXth century a tool to discriminate people, which is one of the role of education (even more so in the XIXth century maybe ?).

There are at least two ways to look at education from a purely economical POV: signal theory (I take someone from Harvard because he was able to go to Harvard) vs human capital theory (I take someone from Harvard because of the things he learned at Harvard).

Of course, there are still many more aspects to it: I take someone at Harvard because he met people at Harvard... and I am myself coming from Harvard, etc...

More simply, I am glad most of what I have learned was "useless" in some sense. What's useful or not changes in times, you cannot necessarily know what's useful to you when you're 15, and you could argue that one of the role of education is to teach you things you will never see otherwise (to expand your horizon).

Not likely, definitely. Veblen wrote about Latin being used for that purpose in 1898 in The Theory of the Leisure Class.

The point of Latin was that it is the root of many European languages, so by studying it early on in education, you would later more easily be able to pick up one of its descendents.

However it is much more efficient to take a course in etymology (word roots) focused on the subset of Greek and Latin used in word formation in the major European languages (Romance or not) than it is to learn a lot of Latin and Greek just for that side benefit. I by no means disparage learning languages--I majored in Chinese and studied two forms of Greek in university, among several other languages--but if the goal is learning etymology, today there are royal roads for that purpose that can be traveled by people who never practice reading Latin or Greek texts.

The general observation is that learning ANY language eases learning the third and the fourth language, because the earliest experience in learning a non-native language reminds the speaker that each language has arbitrary features that must be distinguished from those of the learner's native language(s). Within the ambit of that general principle, learning cognate languages (for example, German for an English speaker) is easier that learning non-cognate languages (for example, Malay for a Chinese speaker).

That's probably true if you're an adult, but how do you motivate kids to learn etmology? At least with Latin there is stuff you can read.

So, by spending years learning Latin, I save... months learning another (European) language. I see.

You seem confused. I am not advocating this, merely explaining it.

Here are the reasons why one would learn Latin.

1. Converse with the great ideas of the past directly (definitely still true.)

2. Enrich one's mind by learning a superior language (like learning Haskell to write better PHP...speak better English by learning Latin. Still true.)

3. Learn a language found everywhere (not so true anymore.)

4. Learn the language of law, medicine and theology (sort of still true.)

5. Learn a foundation to learn Romance languages more quickly, as has been said.

6. Learn it just because it's there and a Renaissance Man has to take a crack at everything. Will be true as long as the language exists!

Finally, I strongly object to the idea that the purpose of Latin is to be "elite." Back then, anyone who went to school would at least learn a little Latin. So, you can say the purpose of having school is to be elite but not the purpose of Latin, because Latin wasn't taught to a subset of children until the 20th century. Today, Latin is taught to anyone who wants to learn, regardless of whether they go to school. My wife is a Latin tutor and about half of her students are below the poverty line or minorities -- and several adults are also receiving instruction from her.

  > Perhaps I'm preaching to the choir, but learning about
  > entrepreneurship or practicing selling things would have
  > been much more useful to me than many of the things I
  > learned in high school or undergrad.

Does that have anything to do with your current life goals, by any chance?

You shouldn't argue from your personal viewpoint here. Sure, in retrospect it would've been great if school had taught me statistics and neurobiology from year one. But that is not what general, state-sanctioned education is or should be about. I suspect that for 80% all kids, entrepreneurship classes would have been a costly waste of time.

I've just applied to university, and it's interesting to see how the maths questions have changed. For example, there are a lot of questions on calculating fractions. Nowadays this would no time at all to work out (put it in a calculator), but back then you would be expected to be able to calculate it mentally, with written notes.

It's strange how as the technology used to solve mathematical problems changes, the ways in which mathematical ability is measured changes too.

The Latin part (1st one) is very simple. The Latin high-school final exam here in Italy is way more difficult (you translate, analyze and discuss Latin authors from their original texts, eg. Cicero is tricky).

As schrototo said the greek part should be as easy.

Am I just being an engineer, or is the math way easier than the rest of this test?

Probably. Coming from the same perspective, I agree.

I'd say some of it is pointlessly tedious, though, such as the one with manual division.

My maths is relatively weak, and I found the maths component trivially easy. Perhaps mathematics had a smaller part to play in society at this stage, because asking a university level student what a prime number is or how to do long division seems trivial.

Doing cube root by hand is more tricky though.

I'd characterize it as 'pointless tedium' and I'm glad our educational system is rid of it. It's easier to justify teaching Latin than that drudgery.

Of course if you're doing it by trial and error on paper it is pointless tedium. But I'm sure that the point of doing these exercises were not bore you to death, but to really make you understand arithmetic so you can do most given problems faster. If all you knew was how to multiply and divide numbers by hand, that problem would take you hours to solve!

A great example is the section 'lucky numbers' in Feynman's book:

http://lib.ru/ANEKDOTY/FEINMAN/feinman_engl.txt

True enough, except it's also along the lines of memorizing the works of Cicero or knowing all of the books of the Bible off by heart: It's useful at developing a skill that the correct tools render obsolete (cheap books in the case of the memory feats, computers in the case of the arithmetical ones). Similarly, knowing Latin and Greek had a purely practical motive as well back then: It marked you as a member of the social elite, defined as people who had enough leisure to study objectively useless things such as Latin and Greek. Memorizing paradigms wasn't something a farmer's son could be expected to do, after all.

I suppose my point, which I expressed poorly, is that it can be interesting to examine how technology impacts coursework.

> that problem would take you hours to solve

I don't know, two Newton iterations are enough:

  *GHCi> let croot f x = x - (x^3 - f) / (3*x^2) in take 5 . iterate (croot 0.0093) $ 0.2
  [0.2,0.21083333333333332,0.2102957483409451,0.2102943717551532,0.21029437174614204]

Guessing 0.2 as a starting point is obvious enough because 0.2^3 = 0.008.

I teach mathematics at a community college and I can tell you that for most people the mathematics on the test is hard. Our course with the largest number of students is on arithmetic and the students just don't comprehend fractions. They can't even comprehend how to convert a decimal to a percent. Especially when given a problem like:

Conver 0.25% to a decimal. That really throws them off.

While I understand this question, I think it is a bit of a trick. I think it would make more sense to ask them to convert 1.25% to a decimal, or any percentage that did not have leading zeros.

I think it is important for one to be able to follow instructions even if they might appear counterintuitive. The rule for conversion is to divide by 100. It doesn't matter what percentage I give you; always divide by 100. It's fairly straightforward but many people are unable to do so in the case of 0.25%. They expect the answer to be 25.

It's not a trick. It requires critical thinking skills, and that a student internalizes concepts like percentages, decimals and fractions.

I've heard from folks in retail finance that large segments of American society do not understand the concept of an interest rate. Everything is just "what is my monthly payment?"

I talked to a fellow CS major Thursday evening and he said he hated all the math involved with the CS program, and that he' failed Pre-Calculus & Trigonometry I three times. This came out after he was complaining about his discrete computational structures class being "nothing but proofs".

If you don't like the math, why get a CS degree? Get a physical science degree and learn how to code on your own time.

Physical science probably won't be much better if you don't like math. Remember, "The book of nature is written in the language of mathematics". Heck, be a humanities major and learn to code, it's not like computers only work for people with technical degrees (though I suspect the training in rigorous thinking helps).

After a lecture and doing several examples I a majority of my college algebra students couldn't do this problem.

You have a house that you bought for $120,000. You sell the house for $173,000 and the real estate commission is 6%. As the seller of the house you have to pay the real estate commission. The real estate commission is an expense and is not counted as part of your profit from the sale of the house. You have to pay a tax of 30% on the profit from the sale of the house. How much tax is paid?

They just couldn't grasp that the real estate commission was not part of their profit. I got the impression that the students believe that the real estate commission is not an expense.

I do believe that a large percentage of society does not understand interest.

Have a look at the UK's STEP mathematics papers. They're the toughest school-level exams we have, used as entrance tests for a handful of degree courses. There are three papers each year, in increasing level of difficulty and assumed knowledge, and each candidate takes papers I and II or papers II and III.

http://www.admissionstests.cambridgeassessment.org.uk/adt/st...

Thanks for sharing that... I found the paper from 1998 that I took... I don't remember how to answer any of the questions anymore which is pretty scary given I did OK back then!!

Some problems are quite fun, but they spoil them with clues -- it does not feel like solving, more like explaining the solution.

Easy with a calculator yes, without one, not so much.

Math transcends time and often language.

It also helps that the field of math has expanded and progressed a decent amount since the time of the exam, (i.e. what was cutting edge and difficult then is common knowledge now) while the fields of Latin and History haven't progressed so much as just gotten older.

Arty type here. I found the history/geography section way easier. But in saying that, I did get the feeling that a lot of the maths would have been trivial if I'd even just briefly studied it.

This is not the entrance exam for math majors, it's the entrance exam for everyone. The math is much more difficult than the entrance exams I took, though mine did offer sections on a broader set of topics, if you were familiar, to let you place out of courses.

The stamp says 1899, but it says 1869 at the bottom of each page. Is it actually from 1869?

The test is from 1869, but the stamp indicates that it was placed in the archive in 1899.

It's fascinating to think that in 1869 there were Transatlantic telegraph links. One could have sat this entrance exam in London while it was being sat in MA simultaneously, with Questions/Answers transmitted digitally.

What was the bandwidth of that telegraph link? And what were the clerical procedures for passing message text from a sending client to the telegraph operator at the sending end, and from the the telegraph operator to the recipient at the receiving end? Just how simultaneous was communication after the trans-Atlantic telegraph cable was laid? Much faster than any ship, surely, but fast enough (and inexpensive enough for most people?) for cheating on a Harvard entrance examination?

First contact was made in 1858, but the cable failed in mere days. The first reliable link happened in 1866. It ran about half "telegraph speed", which was pretty darn slow. I'd hate to connect to that bbs.

It's a fascinating read.

http://en.wikipedia.org/wiki/Transatlantic_telegraph_cable

Slow, but amazing at the same time. I love thinking about things like this.

I remember someone calling my old BBS, back in the early 90s, with a TDD to see what would happen. That explained why I had been seeing 300bps callers when I was used to seeing 1200bps-2400bps.

I recall one holiday starting the download of a picture of a bear. I then went and had Thanksgiving dinner with my family for about two hours. I arrived home just in time for the picture to finish downloading. :P

I completely remember those gifs coming in one agonizing line after the other, except mine were... uuh.. Also bears.

They give almost all the words. I've had harder Latin tests.

The history stuff is weirdly worded. Probably the hardest part of the test.

Hurray for algebra! Still as relevant today as it was a hundred years ago.

Are programming languages going to be equally durable?

That's the goal of Arc. :)

It would have to become relevant first though. I conjecture that no programming language alive now is going to be relevant in 100 years. If you look at the history of programming languages, this is not at all a bold conjecture.

Lisp, Fortran, Cobol have all been used and working, in one form or another, for more than 50 years.

Algol, on the other hand, has evolved into a great family of languages. Not unlike Latin, if I might say so.

Algebra reached its current durable form after centuries of development out of the verbally posed form it was in in the writings of Al-Khwarizmi. So hurrah for letters for unknown quantities (and the convention that "variables" are represented by one set of letters, usually, while "constants" are represented by a distinct set of letters, usually) and hurrah for explicit symbols for arithmetic operations. (I would also say hurrah for Descartes and analytic geometry, which does a lot to make algebra more comprehensible for many visual learners.)

The font reminds me of TeX.

Knuth's fonts were meant to model http://en.wikipedia.org/wiki/Hot_metal_typesetting .

This is really interesting especially given that Harvard now offers "Counting People" and "Magic of Numbers" as classes that satisfy the math (quantitative reasoning) requirement. That's not to say the requirements are better or worse than 100 years ago, it's just interesting how much broader the course offerings are now. You could avoid math, and I know people who did, if you didn't want to take it. And of course, almost no one knows Latin or Greek.

Why does it say "July, 1869" at the bottom?

Were they using the same set of questions for 30 years, or was it put in the library 30 years after it was used?

Good question. I would hazard a guess that they revised the test every year, but didn't want to put the more recent copies of it in the library as they'd be similar, and could poison the results. And therefore they held back old versions as "secret" for, say, 30 years. (Thus your later case, that the test was placed in the library 30 years after it was used.)

Or perhaps this was lost under someone's desk for 30 years in the admissions department, and when they moved into new offices they said "we should put this in the library for posterity's sake."

This doesn't look too bad. But, like any test, it would depend on the time limit and one's expectations going in.

Makes the SAT look like a joke...

And it is, to many Harvard grads.

Maybe I'm out of line but none of that looks too difficult. I studied a (spoken) language at school and was tested on that. Learning Latin isn't too different. The mathematical elements of the test looked straightforward.

Interesting. The Math section with today's GRE exam makes the latter seem like a kindergarten exam.

Graduate students from China (in such humanities subjects as philosophy) derided the GRE main test mathematics section (used as one element of admission decisions for graduate schools in the United States) as a test of "junior high math," which it literally is in terms of the standard curriculum of urban schools in China. The GRE subject test in mathematics, used largely but not exclusively for admission into graduate programs in mathematics, actually has some undergraduate mathematics content, but the mathematics section of the general GRE includes only mathematics that any well educated person who completed secondary schooling ought to know.

FYI, most graduate students I know here in the US also consider the math section in the GRE to be a joke. But as a grad student in an engineering school I guess that's to be expected.

When I took the GRE, the hardest thing about the math test was having to remember long division, since we couldn't use calculators.

Honestly, math section of this 1869 test is still kind of joke for Chinese high school students. Getting full mark is easy for those well educated middle school students, say, up to about 30 percent won't be a overstated figure.

Tuition was probably also around $100 back then. My how we've 'progressed'.

According to [1] tuition was $150 in 1900. According to [2] average annual wage was $450. Assuming women in the work place was a lot less common I will bump it to $500. So about 30% of household income? Harvard costs $34,976 in 2010. According to [3] median household income in 2009? is $49,777. So 70% of median income.

Prices as a percentage of average income has certainly gotten steeper but you cannot argue that things now are less open than they used to be. There are more women and minorities and scholarship opportunities for different groups. Certainly things could be a lot better but progress has surely been made. You can't throw a number like $100 without context.

[1] http://kwharbaugh.blogspot.com/2005/02/educational-costs.htm...

[2] http://usa.usembassy.de/etexts/his/e_prices1.htm

[3] http://en.wikipedia.org/wiki/Median_household_income

It is under-appreciated how open Harvard, Yale, etc, have gotten in modern times. While tuition at Harvard might be 70% of the median annual income today, someone whose family makes $50k/year pays nothing in tuition. At Yale between $60k-$120k, tuition is held at about 10% of family income. Full tuition doesn't phase in until well over $200k.

My brother is at Yale, and his classmates are by and large the children of upper middle class professionals. Certainly kids who've gotten a good shake in life, but mostly people who got in because of good SAT scores and extracurriculars, not donations or political connections.

Original article here is worth reading: http://thechoice.blogs.nytimes.com/2011/03/31/remembering-wh...

Notes that... "of the 210 candidates who took its 1870 test the June before, 185 were admitted."

Also, according to the NYT, this is the 1869 exam, not the 1899 exam (maybe it was added to the library in 1899, hence the stamp?)

It also says 1969 on the bottom of the last page

Erm - 1869 :)

Anyone know what the time limit on the test is?

The maths is so easy I want a vintage 1900 Harvard diploma.

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