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Response to checklist

Original response, written in black, done by Kate 15:16, 7 July 2011 (UTC) Chris 7.9.11 Very strong page. My edits are now simply for clarity and conciseness.

References and footnotes

  • Images cited on click-through
  • No direct quotes used
  • All information is general enough that it appears on most sources that talk about this material, so no footnotes are used, but…
  • The two most helpful online sources are listed at the bottom.

Good writing

Quality of prose and page structuring

  • Beginning paragraphs provide a short definition of the concept
  • Further sections provide examples of ways the concept has been implemented, headings and first sentences make it clear that this is the purpose of these sections

Chris 7.9.11 What is a Base-positional system? Paragraph #1, Sententce #2 In such a system, a "symbol's value depends on its position."

Kate 17:29, 11 July 2011 (UTC): "a symbol's value" doesn't mean the same thing as "the meaning of a group of symbols", and I am intentionally talking about the interpretation of the number as a whole. I did change it back to "depends on" though.

P1S3 ...the symbol 6 [I would switch the examples so that it begins with sameness (625 and 699) and ends with difference (625 and 2,036). It's also better parallelism with the next sentence.

Kate 17:29, 11 July 2011 (UTC): Changed.

P2S2 Change the dash to a semicolon, which is used when separating two complete sentences that need to be combined.

Kate 17:29, 11 July 2011 (UTC): Actually, I really don't think that a semicolon should be used there, as I intended to connect the second part as more of a parenthetical. I just separated them into different sentences to get around the issue.

P3S3: To avoid using the word "number" three times, change the first "number" to "amount."

Kate 17:29, 11 July 2011 (UTC): Changed.

Base Ten System

P1S2 Neither comma is necessary.

Kate 17:29, 11 July 2011 (UTC): I don't think the sentence would read well with the two commas deleted. I split the bit after the "and" into its own sentence, but I'm not getting rid of the remaining comma - although the sentence would be grammatical without it, it is certainly not ungrammatical with it, and I think it improves rather than hinders the flow of the sentence.

Binary P1S1 Remove "that's."

Kate 17:29, 11 July 2011 (UTC): Changed.

Integration of images and text

  • Images relevant to the text are explicitly referred to.
  • Captions and text are used to explain images

Links to other pages

  • Quipu page shows up in the template box in the corner, and is also linked to from the body of the page

Examples, Calculations, Applications, Proofs

  • Numerical examples used in all relevant sections
  • There are no applicable proofs
  • Although base-positional systems are important to pretty much all aspects of modern math, "ways in which the content of the page is useful in larger problems" have not been included for the sake of brevity

Abram, 7/12: In your examples in base 10, could you add a reminder that 1,000 is 10^3, that 100 is 10^2, and that 10 is 10^1. It's not that most readers won't know this, but that they will forget to recall that this is the case.

Mathematical Accuracy and precision of language

  • All mathematical statements are accurate to the best of my knowledge.
  • Prof. Maurer read the page and made several corrections for the sake of accuracy and precision, and I believe that although the page has changed a little since he read it, it's still correct.

Abram, 7/12: I really like what you did with the introductory language for the most part. I'm still not thrilled with the sentence, "Other advantages...." at the end of the first section, for two reasons. First, these aren't unique to positional systems (e.g. the system where 2221 = 7, 2222 = 8, etc.). Second, I'm not sure why the larger numbers corresponding to more symbols is an advantage, as opposed to just a feature.


  • Paragraphs are short, with the exception of the two that describe how to read Mayan and Babylonian number systems, which aren't broken up because I didn't see a good place to split it - if you cut a paragraph in the middle of the explanation, it can look as though you think you are done explaining
  • No mouseovers or hide/shows are used, but I don't think they're necessary - there's not a lot of confusing terminology, and the page is quite short without anything being hidden
  • Page has been viewed in a variety of window sizes, white space and image layout looks good.

Pre-FinalReview Comments

Chris 7/1/11 While I very much like Anna's approach to editing by using the helper checklist, for this edit I am going to comment specifically on the wording. Overall, I like the page very much; it is clearly written, the scope is not too large or small, and the visuals integrate well with the text.

Abram, 7/4/11 I agree with all of the positive things Chris noticed about the page. The specific examples and properties of base-positional systems you chose to focus flesh out the topic well without being overwhelming. See below for a bit more on Chris's suggestions.

Here are the specific issues:

1.1: The meaning of a number does not depend solely on its position. If a 6 and a 4 occupy the same position in different numbers, they have different meanings. Maybe: "the position of a symbol affects its value."

Kate 14:01, 5 July 2011 (UTC): Good point, wording changed.

1.1 Are Roman numerals completely non-positional, given that position sometimes makes a difference?

Kate 14:01, 5 July 2011 (UTC): Roman numerals are the "traditional" example of a non-positional system - position makes a difference, but not in the same way. I'll try and be more careful with my wording here.

1.2 : I would change "size of a number's written representation" to the "amount of symbols in a number."

I agree that this characterization of Roman Numerals is a bit problematic, though it seems like you could see this in two different ways. You could either say that V has two different meanings -- either "-5" or "+5" depending on the symbols that are around it, in which case, why is it being called non-positional? Or you could say that V means "5" in both cases, and that the operation implicitly connecting the symbols is what changes depending on the symbol sequence.
Even if you go with the first interpretation, maybe it makes sense to begin the next sentence, "The symbol V means something different in VI than in VL, even though it's the first symbol of two symbols in both cases..."

Kate 14:01, 5 July 2011 (UTC): As I said above, the fact that position sometimes matters doesn't make it positional - it is the manner in which the position matters that makes it a positional system or not, and Roman numerals are most definitely not a positional system. I'm going to rewrite this section and hopefully fix it.

2.1 I'm not saying that it's wrong, but it seems a bit strange to have the dash in between base and ten. Was that used consistently (or better yet, explained) in your source material?

Kate 14:01, 5 July 2011 (UTC): I dunno, I guess I just always thought that was they way it was written? Did a quick check on the internet, looks like it's typical to say "base-10" or "base ten", will change things.

4.2 Change "clusters" and "collections" to "lines" of dots.

Kate 14:01, 5 July 2011 (UTC): Done.

4.3 The Babylonian number system: the first sentence is in the present tense, the second sentence is in the past tense.

Kate 14:01, 5 July 2011 (UTC): Fixed.

4.4 The 360 degrees in a circle I thought was related to the fact that there are 365 days in a year. Which source did you get that info from?

Kate 14:01, 5 July 2011 (UTC): Literally every site I read about the Babylonian number system mentioned it (so the one I listed and maybe three or four others that are near the top of a google search). I think it's one of those things where no one is really sure where it came from. Since I said "Many people believe" and not "It is a fact that", I'm comfortable with leaving my sentence as-is.

1.x The first, and especially, the last sentence of this section seem to imply that a limited set of symbols is unique to a base-positional system. A unary system, though (represent the number N with N tally marks), also has a limited set of symbols. In fact, the whole last sentence of the first section applies to a unary system.

Kate 14:01, 5 July 2011 (UTC): I don't see this as a problem? Unary is just base one, so the fact that it fits my criteria for a base-positional system is a good thing.

Base-ten System

Abram, 7/4/11:

Maybe you can ease people into the whole idea of "what power of ten it will be multiplied by". Something like (but you will probably find wording you like better), "The digit furthest to the right represents ones. The next digit to the left represents tens, the next hundreds, etc. You might notice that each place value is a power of 10: ones are 10^0, tens are 10^1, hundreds are 10^2, thousands are 10^3, etc."

Maybe the first sentence should say something like the Arabic number system is the one that's most familiar to us because it's the one we use every day.

Kate 14:01, 5 July 2011 (UTC): Rewrote it.


Abram, 7/4/11:

A translation sentence between exponents and plain English could be helpful here as well, e.g. "So in binary, 101 means 1 four, 0 twos, and 1 one, because 2^2 is 4, 2^1 is 2, and 2^0 is 1. Thus, 101 translated into normal base-10, is (1 x 4) + (0 x 2) + (1 x 1) = 5."

Kate 14:01, 5 July 2011 (UTC): I changed this a little - I left the example with 1001 alone, because I want that to be the same number as I used above, but I elaborated on the 10 example.

Other Bases

Abram, 7/4/11:

In the Mayan section, maybe somewhere put an, "As you can see in Image 2 and 3", or something like that, because as a general rule, it's good to explicitly refer to the image you want readers to connect to. It's especially handy here, as may readers will be able to get everything they need from looking at the picture and can avoid reading the text entirely.

I wonder if it's worth making a bigger deal about the zero and how it's a pain in the butt not to have one. Not like you would add much more content, just maybe it should be separated into its own paragraph. You could show a side by side of the number 40, say, in Mayan, and 120 in Babylonian, and point out how in Mayan it's clear that the number is 40, whereas in Babylonian, it's hard to tell if the number is 2, 61, or 120. If you don't want to bother, that's fine; it just seems like a good opportunity to extoll the virtues of zero.

Kate 14:01, 5 July 2011 (UTC): I'll put in references to the images. I don't really want to go into more detail about zero for two reasons. First, the Babylonian system isn't that unclear - they were pretty careful with their spacing, and there is evidence that (occasionally) some sort of placeholders would be used. Second, while the issue is relevant enough that it should be mentioned, this isn't a page about zero, nor is it a page about the Babylonian number system, and I think one of the good things about this page is that it's short and tightly focused, so I'm gonna keep it this way.

xd 18:48, 10 June 2011 (UTC)I read it. I think it is good. It will be better however, if you can put in some illustrations for the Babylonian number system. If not, that is fine too.

done! I'm going to move this comment to the discussion page in a day or so.
xd 19:52, 10 June 2011 (UTC) cool