Harvard 1869 entrance exam • Hacker News Board

Re: Harvard 1869 entrance exam

#51

Post by michaeldhopkins » Mon, Dec 05, 2011, 3:59 AM UTC

orionhickman wrote: post #13

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.

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.

Re: Harvard 1869 entrance exam

#52

Post by 32ftpersecond » Mon, Dec 05, 2011, 4:03 AM UTC

dexy wrote: post #8

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...

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

Re: Harvard 1869 entrance exam

#53

Post by BrandonM » Mon, Dec 05, 2011, 4:13 AM UTC

baby wrote: post #45

mortenjorck wrote: post #22

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.

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.

> 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.

Re: Harvard 1869 entrance exam

#54

Post by dhconnelly » Mon, Dec 05, 2011, 4:13 AM UTC

baby wrote: post #43

hammock wrote: post #34

Earlier quoted context omitted.

Who here can come up with the most concise explanation?

(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.

this, with the associative law

Re: Harvard 1869 entrance exam

#55

Post by baby » Mon, Dec 05, 2011, 4:22 AM UTC

BrandonM wrote: post #53

baby wrote: post #45

Earlier quoted context omitted.

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.

> 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.

I think this website has a pretty poor UI. And it's PHP also.

Re: Harvard 1869 entrance exam

#56

Post by jerf » Mon, Dec 05, 2011, 4:23 AM UTC

baddox wrote: post #38

cousin_it wrote: post #35

Earlier quoted context omitted.

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)

That's not very rigorous, especially with fractional (or God forbid, irrational) exponents.

Given that the exam is from 1869 for entrance into college, I suspect that's basically what they are looking for.

Re: Harvard 1869 entrance exam

#57

Post by seagaia » Mon, Dec 05, 2011, 4:24 AM UTC

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

Re: Harvard 1869 entrance exam

#58

Post by barrkel » Mon, Dec 05, 2011, 4:25 AM UTC

michaeldhopkins wrote: post #47

baddox wrote: post #37

Earlier quoted context omitted.

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…

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

I don't think that's the case. As baddox says, it's trivial to show it is true, especially using simplified definitions for exponentiation (i.e. sticking with integer or perhaps rational exponents), but demonstrating truth doesn't tell you about the "reason".

Is the question about a philosophical position as to how mathematics relates to God? A "reason" seems to imply a purpose.

Re: Harvard 1869 entrance exam

#59

Post by wvoq » Mon, Dec 05, 2011, 4:25 AM UTC

baby wrote: post #45

mortenjorck wrote: post #22

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.

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.

I care about scheme.

Re: Harvard 1869 entrance exam

#60

Post by barrkel » Mon, Dec 05, 2011, 4:27 AM UTC

ry0ohki wrote: post #6

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

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.