0953: "1 to 10"

[exhnozoaa]

I had a professor at university (in California) who was British in origin (Scottish I think) and used what he claimed was the normal grading scheme out there, which freaked out a lot of his (American) students until he explained it. Seems they don't neglect the bottom half of the numeric scale where he comes from, so a middle grade (passing, "C") out of 10 is a 5, a middle grade out of 100 is 50, etc. 75/100 is a B, 100/100 is a perfect A of course, 25/100 is a D, and 0/100 is of course a fail.

Needless to say, plenty of American students who are used to <60% being a failingly bad grade panicked when assignments came back graded "5/10", only to be assured that no, they are passingly average as a normal sensible non-American person would expect from a grade of half the available points. The professor thought the American system was a product of coddling and making sure that everybody ended up "above average"; I always figured it was because 50% was the noise base, what you would expect from random guessing, and so anything above that indicated a signal of actual knowledge. Does anybody here know the true origin of the American-style system (60 = D, 70 = C, 80 = B, 90 = A)?

My professors seem to like to grade like that (5/10 is more or less average)... But then they pass it on to the 90% A, 80% B, etc. system to make it really hard to do well.

[drazen]

Ugh, it's early. I didn't see the "/100" the first time I read the alt text so all I could think was, "Wait, wouldn't 11 = B in hex?"

Of course, that hypothetical CS professor/TA could always come back at you that it's an F since 11/100 would be about 6% in hex...

[AvatarIII]

2) Since when 10₂ should be pronounced anything other than "two"? 10₂ and 2₁₀ are merely different representations of the same number, namely, "two". I don't see why there should be completely new ways to pronounce numbers in different representations; I mean, is LXXVI pronounced as "el eks eks vee eye", or simply "seventy-six"?

This got me thinking, how exactly did Romans pronounce numbers? I'm guessing they had a word for every numeral notation, then spoke them in order, does anyone know if that's right? do we even know?

[hifi]

This got me thinking, how exactly did Romans pronounce numbers? I'm guessing they had a word for every numeral notation, then spoke them in order, does anyone know if that's right? do we even know?

The only one I know to pronounce is 18 - duodeviginti.

[kiffer]

This got me thinking, how exactly did Romans pronounce numbers? I'm guessing they had a word for every numeral notation, then spoke them in order, does anyone know if that's right? do we even know?

They spoke in base ten basically.
http://www.transparent.com/latin/latin-numbers-1-100/

[AvatarIII]

This got me thinking, how exactly did Romans pronounce numbers? I'm guessing they had a word for every numeral notation, then spoke them in order, does anyone know if that's right? do we even know?

The only one I know to pronounce is 18 - duodeviginti.

i assume that is essentially "two less than twenty",which doesn't really make sense, i would have expected it to be "ten and five and three"

[hifi]

This got me thinking, how exactly did Romans pronounce numbers? I'm guessing they had a word for every numeral notation, then spoke them in order, does anyone know if that's right? do we even know?

The only one I know to pronounce is 18 - duodeviginti.

i assume that is essentially "two less than twenty",which doesn't really make sense, i would have expected it to be "ten and five and three"

True, and the only reason I can think of is that it's shorter this way. However, to ease your furrowed brow, 19 is written and pronounced as '1 less than 20' (according to kiffers link). That said, further reading shows that 21 is pronounced as '1 and twenty' and not 'ten ten one'. So they had a way of saying 20, but not a way of writing it. Interesting..

[Sean Quixote]

It's okay, Bender... There's no such thing as two.

[kaizoman]

Ummm..... 1100100%

[Eebster the Great]

The thing about grades in college is that it doesn't really matter what system they use, because they are usually curved anyway.

Note that a scale that has 25% as a passing grade is pretty problematic for four-choice tests.

[Jeff S]

I have to agree with the folks who say "10" in any base other than decimal should not be pronounced "ten".

"Ten" is an English word expressing a specific *quantity*. It is baseless, and corresponds to the *quantity* which an be expressed in decimal-based notation as "10", in binary as "1010", in hexadecimal as "A", etc. Likewise, all the other numeric English words.

English is simply English, and if you are going to use the English word for a quantity, it represents that quantity, not a notation. At least, that's my opinion, for what it's worth.

So, binary jokes involving mathematical notation in different bases sharing common symbols don't work well when spoken aloud, at least in English.

[Sean Quixote]

Clearly, there are 10 kinds of people in the world, with two differing perceptions of the definition of the word "ten": Some people consider it to be "The integer whose prime factorization is 5*2" (and it is no more seperable from this definition than the number "nine" is from the mathematical definition of "3 squared") while others consider it to be "The number signifying which base system you are currently assuming."

That being established, the next step seems to be standardization of which one which is. Perhaps a completely new word is in order?

[Spiky]

A 70% doesn't mean that you're better than 70% of the class. It means you got 70% of the answers correct. That's not coddling; that's hard statistics. If you know less than 60% of the material, of course you shouldn't be able to pass. That's why such grades are considered failing.

As cream wobbly said, it's all about what the exam is setting out to measure. I was educated in the UK and my experience mirrored his: Examinations were not simply seeing if you could regurgitate knowledge but measuring your capacity to apply said knowledge in novel and challenging ways - without assistance and under time pressure; That being a far more useful goal for education than simple regurgitation, of course.

So, yeah, if it's nothing more than a knowledge regurgitation exercise, then, yeah, perhaps 60% would be a poor result. But if the exam consists of a sliding scale of questions from easy to genius level then you can see at what point a particular student starts getting the answers wrong, and, in that case, 60% might be very acceptable.

It also makes for a much more useful measurement from the school's point of view, since it can determine if someone needs extra assistance to learn the basics, or if they could do with being put in advanced classes to learn more quickly to prevent boredom. An A grade at 90% is like having an IQ test that maxes out at 120 - it doesn't differentiate the top end enough (should you care about that - which, admittedly, many schools seemingly don't).

This is why I liked the classes that graded on a curve. Skew the results, just for fun! Made little difference for some, others disliked it, though.

[Anonymously Famous]

I had classes that "graded on a curve," but they didn't really. They didn't standardize the curve given the distribution of the scores, but simply made the highest score in the class 100%.

The other students in the class didn't really like the students on the high end...

[SamSam]

True, and the only reason I can think of is that it's shorter this way. However, to ease your furrowed brow, 19 is written and pronounced as '1 less than 20' (according to kiffers link). That said, further reading shows that 21 is pronounced as '1 and twenty' and not 'ten ten one'. So they had a way of saying 20, but not a way of writing it. Interesting..

Well, is that any weirder than French, which has a way of writing 70, 80 and 90 but not a (simple) way of saying them?

70: Soixante-dix, 80: Quatre-vingts, 90: Quatre-vingt-dix, 99: Quatre-vingt-dix-neuf

Literally: "Sixty-ten," "four twenties," "four twenty ten", "four twenty ten-nine" (or "four twenty nineteen")

They just ran out of names for multiples of ten above 60.

[SamSam]

So they had a way of saying 20, but not a way of writing it. Interesting..

But actually, to go back to this, of course they had a way of saying 20, and they had a way of writing it.

First, of course they had a way of saying it, since spoken language predates written language and people were almost certainly referring to twenty (which isn't that high after all) long before they were writing it.

Second, using 20 (2^{x 10}+0^{x 1}) is just as arbitrary as using XX (X(^{(i.e. 10)}+X(^{(i.e. 10)}). It's all just written notation. Sure, the Arabic number system makes math much easier, but there's no more reason to be surprised that XX is pronounced "viginti" than that 20 is pronounced "twenty." There's nothing "twenty-ish" about the characters 2 and 0. That's just the way we chose to write the number twenty which, again, we were talking about before we were writing it.

And anyway, where do you think we got the word "twenty" from? Notice any similarities between "twenty" and the "venti" that you might order at Starbucks? (It went through German along the way, but the root is the same).

[Sean Quixote]

Wow. So is 420 in France really 99?

Speaking of which, it's almost weed-thirty...

[jpk]

Since we're talking about different numerical bases, here's a fun little problem:

We all remember the rule from grade school that the digital root of a multiple of 9 will always be 9, and a number whose digital root is 9 is a mutiple of 9. Thus 2736 is a multiple of 9 (2+7+6+3 = 18, 1+8 =9), and the product of 2736 * 81 (whatever it is) will have a digital root of 9. Does this generalize to bases other than base 10, and why or why not?

[Sean Quixote]

I've never heard of that rule before, but judging by context clues I would have to guess that it has a lot to do with the fact that the digits of all multiples of three (in all bases, too, I believe?) also add up to multiples of three.

Tesla is probably rolling over in his grave... but in a good way.

Edit: Blah! "Digital root," I didn't know that's what it was called, either. =\

[Pfhorrest]

This got me thinking, how exactly did Romans pronounce numbers? I'm guessing they had a word for every numeral notation, then spoke them in order, does anyone know if that's right? do we even know?

The only one I know to pronounce is 18 - duodeviginti.

i assume that is essentially "two less than twenty",which doesn't really make sense, i would have expected it to be "ten and five and three"

True, and the only reason I can think of is that it's shorter this way. However, to ease your furrowed brow, 19 is written and pronounced as '1 less than 20' (according to kiffers link). That said, further reading shows that 21 is pronounced as '1 and twenty' and not 'ten ten one'. So they had a way of saying 20, but not a way of writing it. Interesting..

You may notice there is a pattern to the multiples-of-ten words:

vīgintī
trīgintā
quadrāgintā
quīnquāgintā
sexāgintā
septuāgintā
octōgintā
nōnāgintā

Hmm... nona, octo, septua, sexa, quinqua, quadra, tri... and with how v is pronounced in Latin it's not a far slur from a b, so bi. It's almost like these words are saying two-tens, three-tens, four-tens, etc. So duodeviginti is "two less than two tens", unus et viginti is "one and two tens". Not so surprising now?

Also note that the "a couple less than" pattern is used in the written numbers in places where there exists a unique word for the number, for example quattuor = IV (I less than V). I wouldn't be at all surprised if IIXX was comprehensible, if ungrammatical, to a Roman as equivalent to XXVIII. After all they've already got IX as shorthand for XVIIII.

[branko623]

1) Seriously, is this comic nothing but a base-2 joke? Really, any regular CS student must have heard a joke like that hundreds of times in the duration of a regular course. Every iota of humour out of that joke has already been extracted, and Randall's variation adds nothing, absolutely NOTHING to it. He's offering us stale bread, and without even bothering to add a lousy layer of butter.

hate to say it but.... ^This

surprised that not as many people have said this, are there not as many CS people reading these? unless im missing something, felt kinda lame.

I kinda liked the alt though!

[gmalivuk]

The question was, "...how likely is it...?" Questions of probability should always be answered on a scale from 0 to 1.

I'd just like to pop in to state that I agree with this statement.

Nonsense. Odds can be any positive real number.

Does this generalize to bases other than base 10, and why or why not?

The principle generalizes, yes, and for the same reason it works with 9 in base 9+1.

the digits of all multiples of three (in all bases, too, I believe?) also add up to multiples of three.

Simple counterexample: in base-3 all the powers of 3 have digits that add to 1, on account of all being 1 followed by some 0's.

[Anonymously Famous]

The question was, "...how likely is it...?" Questions of probability should always be answered on a scale from 0 to 1.

I'd just like to pop in to state that I agree with this statement.

Nonsense. Odds can be any positive real number.

Upon further reflection, you are, of course, right.

The question was not "What is the probability..." in which case 0 <= p <= 1, but was "Given this certain way of measuring likelihood, how likely is...". "What are the odds of..." would have an answer similar to "6:1," using the example of days in the week mentioned in the Wiki article that you cited.

[Yaten13]

I think the real problem is asking for a probability in binary. A scale of 1-10 (binary) still translates to only two choices (0% or 100% probability) which is a useless scale for expressing uncertainty.

Which doesn't even start to question why a binary (binary) scale would use two bits of information, when a single bit would do, which means that either the questioner is not using binary, or is using it inefficiently.

[ancalime]

Shouldn't you claim to get a B? If you are claiming to get a 11 out of 100 in binary then asking for C means there would be no way of getting a B. Assuming 4/4 is an A, if 3/4 is a C, how would you be able to get a B?

[Yaten13]

I had classes that "graded on a curve," but they didn't really. They didn't standardize the curve given the distribution of the scores, but simply made the highest score in the class 100%.

The other students in the class didn't really like the students on the high end...

I was also graded on a curve in large science classes, but if you are graded on a curve, they set the mean as a certain grade (eg C, or sometimes B- if the prof was nice), then you were assigned grades based on a standard deviation. Eg. C is mean +/- 1 s.d., B is up to +2, D is -2, etc.

[john.m.law]

10 in binary is not pronounced "ten", it's either "two" or "one-zero". "Ten" is defined by the OED as "the cardinal number next higher than nine". If you say ten base two then you mean 1010, not 10.

The t-shirt should read "There are 11 types of people in the world, those who understand binary, those who don't and those who insist the number above is pronounced as eleven no matter what base you're in".

Way to fail with your first post. A binary 11 is 0x03.

He knows that. You should stop posting now =)

[Pfhorrest]

I had classes that "graded on a curve," but they didn't really. They didn't standardize the curve given the distribution of the scores, but simply made the highest score in the class 100%.

The other students in the class didn't really like the students on the high end...

My very first course in college was even worse than that. Worst grading system I have ever seen. The teacher graded on a curve calibrated to the grade distribution of that particular test. Meaning after the first midterm, students in the bottom half-ish (assuming a normal distribution), failing that midterm, withdrew from that class. Then after the next midterm, half-ish of the remaining students failed that midterm and withdrew from the class. And likewise the next, and so on. Out of a class of 30-something people I think we ended up with 5-7 by the end. Made me kind of proud to be one of the few survivors*, but man, what a bone-headed system.

*(He also ranted as the final papers were handed back that "a lot of people obviously stayed up and wrote this the night before it was due. I tell every class, every term, nobody ever writes a paper the night before it's due and gets full marks..." prompting me to interject "I did").

Shouldn't you claim to get a B? If you are claiming to get a 11 out of 100 in binary then asking for C means there would be no way of getting a B. Assuming 4/4 is an A, if 3/4 is a C, how would you be able to get a B?

If you're using a three-digit binary number to represent grades, from 0 to 100, and the usual (American) grading where every 10% above 50% puts you in range of the next higher letter grade, then there is no room for B's, nor D's. 100 = 100% = A, 11 = 75% = C, 10 or below = ≤50% = F. Which is a good argument for not using that grading scheme, at least on such a small scale. GPA is (usually) a four-point scale too, with 4 (100_2) = A, 3 (11_2) = B, 2 (10_2) = C, 1 = D, and 0 = F

[ijuin]

A 70% doesn't mean that you're better than 70% of the class. It means you got 70% of the answers correct. That's not coddling; that's hard statistics. If you know less than 60% of the material, of course you shouldn't be able to pass. That's why such grades are considered failing.

As cream wobbly said, it's all about what the exam is setting out to measure. I was educated in the UK and my experience mirrored his: Examinations were not simply seeing if you could regurgitate knowledge but measuring your capacity to apply said knowledge in novel and challenging ways - without assistance and under time pressure; That being a far more useful goal for education than simple regurgitation, of course.

So, yeah, if it's nothing more than a knowledge regurgitation exercise, then, yeah, perhaps 60% would be a poor result. But if the exam consists of a sliding scale of questions from easy to genius level then you can see at what point a particular student starts getting the answers wrong, and, in that case, 60% might be very acceptable.

It also makes for a much more useful measurement from the school's point of view, since it can determine if someone needs extra assistance to learn the basics, or if they could do with being put in advanced classes to learn more quickly to prevent boredom. An A grade at 90% is like having an IQ test that maxes out at 120 - it doesn't differentiate the top end enough (should you care about that - which, admittedly, many schools seemingly don't).

The schools that I attended (public schools in California) generally went by the standard of "any shortfall from a perfect score is a sign that you haven't learned everything expected".

[alextrabec]

Bender would have freaked out and said 21!

[AvatarIII]

So they had a way of saying 20, but not a way of writing it. Interesting..

But actually, to go back to this, of course they had a way of saying 20, and they had a way of writing it.

First, of course they had a way of saying it, since spoken language predates written language and people were almost certainly referring to twenty (which isn't that high after all) long before they were writing it.

Second, using 20 (2^{x 10}+0^{x 1}) is just as arbitrary as using XX (X(^{(i.e. 10)}+X(^{(i.e. 10)}). It's all just written notation. Sure, the Arabic number system makes math much easier, but there's no more reason to be surprised that XX is pronounced "viginti" than that 20 is pronounced "twenty." There's nothing "twenty-ish" about the characters 2 and 0. That's just the way we chose to write the number twenty which, again, we were talking about before we were writing it.

And anyway, where do you think we got the word "twenty" from? Notice any similarities between "twenty" and the "venti" that you might order at Starbucks? (It went through German along the way, but the root is the same).

i dunno, Twenty, Two-and-oh, Two-anto, Two-ento, Two-enty- Twenty

[scarletmanuka]

Also, 1.111 is a pretty good answer to the question.

Came here planning to post that. Though I'd have made it recurring, for improved accuracy in the binary case.

wouldn't 1.111 recurring in binary be 1.999 recurring in decimal? that was what i would have figured anyway.

Yes, it would. But what you are neglecting is that 10 in binary is 2 in decimal. And 1.999 recurring is equal to 2. So, if the question is in binary, the answer would be "2 out of 2" in decimal, or "10 out of 10" in binary. If the question is not in binary, the answer is "1 1/9 out of (whatever base we are using)" in decimal.

[jpk]

The schools that I attended (public schools in California) generally went by the standard of "any shortfall from a perfect score is a sign that you haven't learned everything expected".

On the other hand, I've had teachers who treated "learning everything expected" as simply doing B-grade work. 'A' was reserved for people who excelled, not for those who merely lived up to expectations. Those were some of my favorite teachers - it's nice to work with someone who actually expects their students to learn something.

[dvrvm]

The answer to the question is 1, obviously.

[SchighSchagh]

"What's a 4?", she asks.
I say, "guaranteed to be random".

[elasto]

The schools that I attended (public schools in California) generally went by the standard of "any shortfall from a perfect score is a sign that you haven't learned everything expected".

On the other hand, I've had teachers who treated "learning everything expected" as simply doing B-grade work. 'A' was reserved for people who excelled, not for those who merely lived up to expectations. Those were some of my favorite teachers - it's nice to work with someone who actually expects their students to learn something.

Indeed. There are plenty of areas of a good education where 'learning everything expected' is only the beginning.

In an English class, your spelling and grammar may be flawless - but how good are you at writing a short story? Your story might only get 70% but that might be a perfectly acceptable score (hence warranting an A). The remainder of 70-100% can be used to distinguish a merely good story from a rip-roaring yarn.

[Age of Fable]

Since she's presumably already made the decision whether to use binary, the chance must be either 0 or 1. So in a sense it's definitely binary.

[Kibbles0515]

10 in binary is not pronounced "ten", it's either "two" or "one-zero". "Ten" is defined by the OED as "the cardinal number next higher than nine". If you say ten base two then you mean 1010, not 10.

The t-shirt should read "There are 11 types of people in the world, those who understand binary, those who don't and those who insist the number above is pronounced as eleven no matter what base you're in".

Way to fail with your first post. A binary 11 is 0x03.

They didn't mentioned hex anywhere...binary 11 is 3 decimal or 03 hex, but the only reason that would matter is if you are taking "no matter what base you're in" to imply binary, hex, or decimal...but 0x11 is 18...I think I just confused myself.

[mattme]

A comic drawn in 2007: http://cowbirdsinlove.com/43

[BubblePig]

Since the probability approaches zero (i.e. there are an infinite number of bases to choose from) and the scale does not start at zero, must not the answer be 1?