A dog's garden of versus

After I wrote the previous post on The Moleskine IPO, I saw a hypothetical parallel to the company’s annoying unwillingness to reveal the weight of the paper in their “legendary” pocket notebooks. When the U.S. government mandated disclosure of miles-per-gallon (MPG) ratings for automobiles, marketers immediately followed the lead of the software industry and turned this “bug” into a “feature” — the added workload of satisfying the new regulations was offset by an opportunity to tout the models with the best mileage. Of course, some model ends up at the bottom of that list, and every car buyer can see it. Imagine instead that these disclosures were voluntary, with most manufacturers participating, but that Übermobile demurred because it knew that its best-selling Ω Series would be the bottom-dweller. In short order, blogs and forums on luxury car websites would have anecdotes galore about poor gas mileage. But the official corporate posture would be silence, not to say disdain. Who cares about a few complainers, if affluent or aspiring drivers continue to buy?

Just so there isn’t any doubt, here is the mapping between that hypothetical scenario and my real-world annoyance:
• Übermobile = Moleskine
• Ω Series = Classic Pocket Notebook
• luxury car blogs = Fountain Pen Network
• complainers = fountain pen users
• silence = silence
• MPG = GSM

And “GSM” would be what?…

 

Welcome to PenWorld

Before I answer that, it is important to recognize that we are no longer in the real world. We have moved into what I call “PenWorld,” with its own special opportunities for focus, fantasy, fixation, and fetish. Any domain built around a technology-mediated pursuit allows such a mix. In TabletWorld it is all about apps and styli and covers and bluetooth keyboards and so on. In PenWorld, it is all about nibs and ink and converters and paper — including notebooks — and so on. Talking about all the apps you have on your iPad is the logical equivalent of talking about all the bottles of ink you have in your desk drawer. The surest way to know if you are in one of these places is to notice whether you are easily distracted by the technology itself. Here is a litmus test from ‘Infrared and In Visible’, my post from last year about CameraWorld: “It’s not that the technology is unimportant — the right camera lens or musical instrument or tablet computer or fly rod or fountain pen can be crucial — but that the tool can slowly take primacy over the pursuit it is meant to enable.” You are forewarned.

Now that you are oriented to PenWorld, here is the short answer to the question: “GSM” stands for “grams per square meter,” the units used to express the “weight” of paper. This is particularly important for fountain pen users, because heavier paper generally offers a better writing experience. Things like the ink and the width of the nib where it actually contacts the paper also matter, but the paper itself is a very big deal. Some of the notebooks that I have at hand are imprinted with the GSM weight, or you can find it on the manufacturer’s website:

• Calepino, 90
• Clairefontaine, 90
• Fabriano, 80, 85, 90, 95, 100
• Mossery, 120
• Rhodia (Clairefontaine paper), 80, 90

These are all excellent for fountain pens (or gel rollerballs), especially those at 85 gsm and higher with my favorite nib + ink combinations.

The Bottom Line

And how about Moleskine paper in the Classic Notebooks? As I said above, corporate silence. So we turn to an unofficial value, a simple measurement done by Brian Goulet of The Goulet Pen Company for Episode #11 of The Ink Nouveau podcasts. His result: 72 gsm. This was an excellent back-of-the-envelope approach and would register well on Chip Morningstar’s Goodenoughness Meter. Still, from my lab scientist’s perspective, there was room for a couple of improvements: (1) averaging across a large amount of paper, rather than the single sheet (bifolium) that Brian measured; and (2) increasing the two-significant-figure precision of his measurement. I discuss all this in mind-numbing detail below, including a novel variation on the standard-addition technique from analytical chemistry. A real page-turner from the lab. If you just want my bottom line, however, here it is: the “weight” of Moleskine paper is 71.0 gsm.

If the Moleskine marketing types ever decide to reveal their number, I’m guessing it would be a nice, round 70 gsm, which is probably within the error limits of both Brian’s result and mine. Good enough indeed.

Until that unlikely millennial event, what do you do? Easy. Use 70 gsm (rounded down to one significant figure) or 71.0 (my value) or 72 (Brian’s) as a reference point for standard Moleskine paper. If you are a newcomer to all this, buy an inexpensive fountain pen — my suggestion and totally unsolicited endorsement would be a Lamy Safari from The Goulet Pen Company with a Medium nib and a converter. Find an ink in The Swab Shop that appeals to you and add that to your order. Now write a lot on a variety of papers. Hopefully some of them will be 85-100 gsm, like the ones I listed above; maybe even try some 120-gsm heavyweights or sketch papers. Go the other direction as well and get some lowly copier paper. One sheet should do it. If the wrapper says “20# bond” or the like, you can try to convert to GSM weight with a table like this. Good luck with that. And get a “legendary” Classic Notebook from Moleskine, which is available at eight bzillion places worldwide. Keep track of the differences among all those papers. If you don’t see any difference, then that’s OK too, but odds are that you will. Look at the ones you like writing on, and see if there is a threshhold GSM weight that you need to be above. Odds are there will be, 80 gsm or higher just at a guess. And then never look back. Life is good in PenWorld.

I was going to end by acknowledging my debt to Brian Goulet with the quote often attributed to Isaac Newton — “If I have seen further it is by standing on the shoulders of giants.” But I decided it was presumptuous, over-the-top, and self-ingratiating. After all, this is the guy from whom I buy ink, notebooks, and the occasional pen. Yet it did make me realize something else. If you have watched any of the Ink Nouveau podcasts in which Brian reviews pens, he almost always points out that the pen looks small because “I have giant hands.” Maybe he’s trying to reveal something…. Think about it, have you ever seen anyone else (except his wife Rachel) in any of the videos?… Maybe what he is really saying is “I am a giant.” Wow. So I can use Newton’s quote without presumption or exaggeration (although there may be a tiny bit of ingratiation). Thanks, Brian!

That’s also the end of the story, except for the promised mind-numbing detail. But, if you really want more, then, to paraphrase Brian’s standard sign-off: “Read On.”

---

“And now for something completely analytical!”

If you don’t believe me about the “mind-numbing” part, maybe you will after this: there is so much to follow that I split it up into sub-sections, with this mini-table of contents to help those who get lost. That will be pretty much everyone, I suspect. Now you are really forewarned.

• Measurement techniques
• Experimental protocol
• Relaxing a false assumption
• Accounting for the “augmented cover”
• Filling in the numbers
• Calculating the GSM weight of Moleskine paper
• How could there be more?!!!

 

Measurement techniques

Now that the readership is pared down to a couple of lab scientists (Azizah and Iwan, that would be you) and a handful of other hardcore fountain pen aficionados, we can begin by clarifying some definitions. In PenWorld, “GSM weight” has units of grams per square meter (g/m²). It is the widely- though not universally-used measure of paper density, technically an area density. It is not a true weight (and certainly not thickness — sorry, Brian), though it is often incorrectly referred to as “weight.” Some notebooks list the units as “gsm” (Clairefontaine, Mossery); others unfortunately shorten it to “g” or “gr” (Fabriano); and still others use both, depending on the product (Rhodia). In what follows, I will distinguish between weight (g) and “GSM weight” (g/m²), the latter being the parameter that we are documenting here for the Moleskine notebooks.

I used three measuring tools:
• stainless steel rulers, 15 cm (6″) and 30 cm (12″) lengths with 1 mm gradations (C-Thru Models MR-6 and MR-12);
• a digital caliper/micrometer with 15 cm maximum and 0.01 mm resolution (General Tools Ultratech Model No. 147); and
• a digital scale with 2 kg maximum and 1 g resolution (Salter Model 3001, now discontinued).

Let’s be honest. The Salter 3001 was marketed as a postal and kitchen scale. For weighing letters and lettuce. So, if you’re thinking, “Wait a minute, this guy is going to measure the GSM weight of paper with a food scale? And besides, I watched Brian Goulet’s video and his scale had a 0.1 g resolution, so surely that’s better,” then let me mention a few things. Firstly, as a reminder I’m going to measure weight and then calculate GSM weight (just as Brian did). Secondly, I watched that video, too, and I was able to identify his scale. It’s a Salter Brecknell PB500. Same stable, just a different horse, and an excellent one at that. Thirdly, here is the first set of measurements I took to confirm that the one-gram resolution of my scale was adequate:

Those brightly-colored notebooks in the photo farther back up the page are the Fabriano Bouquet Note Pad Set. They are all the same size, same binding, and have 40 sheets (80 sides/pages) each. This graph shows the GSM weight of the paper (printed on the back cover) vs. the weight of the bulk notebook, which I measured on the Salter 3001. Since the papers are all different, the upward trend doesn’t have any particular significance for our purposes, except to confirm that an increase in paper GSM weight leads to a monotonic and (in this case) smooth increase in notebook weight. So no problem with the scale covering the relevant range and resolving common GSM weights.

 

Experimental protocol

To determine the GSM weight of Moleskine paper, my approach was inspired by the standard addition technique from analytical chemistry. In brief, if we have several notebooks with the same dimensions, the same size and composition of paper, and the same cover, but — crucially — with different numbers of sheets/pages, then necessarily the one with the most sheets will weigh the most. In fact, on a plot of number of sheets (x) against weight (y), the relationship should be a simple straight line. (We’ll get to the math for this a little farther down.) Projecting that line back to the y-axis will correspond to a notebook with zero pages. If that seems like a phrase from a Zen koan (how appropriate for this blog!), pause for a moment….

In our context, a notebook with zero pages is just the in-common items of the cover and binding — the black/red leatherette wrap, boards, endpapers, fabric bookmark, back pocket (inserts removed), elastic strap, glue, and thread — everything except the paper, the amount of which is the independent variable that changes (the addition part of the name) along the x-axis. The numerical value of the y-intercept is then the weight of all this cover+binding stuff in grams. The slope is in units of grams/sheet. So if we divide the slope by the area of the standard sheet in the notebooks, we can get the GSM weight of the paper! The beauty of this is that it averages over both more paper and multiple notebooks, so small manufacturing fluctuations and measurement glitches — including things like the holes that inevitably result when you separate sheets from binding in order to weigh them — are smoothed out or avoided altogether. If the whole thing seems almost magical, that’s OK. The first time I encountered the standard addition technique in a lab setting, it looked too good to be true, like the answer was being pulled out of thin air. But I guarantee it isn’t. Take a look at the Wikipedia article (link in the first sentence of the previous paragraph).

 

Relaxing a false assumption

I bought the notebooks in the photo (above, right) because they appeared to satisfy the four assumptions given above:
• same dimensions, nominally 9×14 cm, but with the cover overhanging the sheets (more below);
• same paper, within the precision of my visual and tactile acuity, a fancy way of saying the paper looks and feels the same; and
• same hard covers, ignoring the black vs. red distinction; but
• different numbers of sheets/pages.

The four samples, from top to bottom in the photo to the right, are:
• Weekly Diary/Planner (D/P), 72 sheets (DHB12WV2SE);
• Squared Notebook, 96 sheets (MM712F);
• Weekly D/P — 18 mos (Horizontal), 104 sheets (DHR18WH2SE); and
• Daily D/P, 200 sheets (DHB12DC2SE), on top of the orange Rhodia Webbie, with my Pilot Custom 845 because I wanted to show it off for scale.
I used the three Diary/Planners to test the method and provide a calibration for the Squared Notebook (more below).

I recognized going in that the third assumption had to be false for a simple geometric/topological reason: as the number of sheets increased, the thickness of the paper stack had to increase and therefore the enclosing cover would have to become larger and heavier due to the small increase in the width of the spine. That meant that a graph of number of sheets vs. notebook weight would be concave upward in principle, but I was skeptical that the difference would be observable. Look at the graph below and then color my face about as red as the cover on that 18-month Planner!

The effect of the “augmented cover” is easily observable by comparing the best-fit second-order polynomial (solid) with the straight line (dashed), arbitrarily positioned to emphasize the curvature relative to extrapolation from the smallest notebook. Here are all the raw data:
• Weekly D/P: 72 sheets, 110 g (total weight)
• Weekly D/P — 18 mos: 104 sheets, 134 g
• Daily D/P: 200 sheets, 223 g

 

Accounting for the “augmented cover”

For the original assumption of identical covers, the total weight of the ith notebook is:

W_i = N_iW_S+ C

where N_i is the number of sheets in the ith notebook, W_S is the weight of a standard sheet, and C is the weight of the cover. With the variable size of the covers, however, C must be changed to C_i, with a different value for each notebook:

W_i = N_iW_S + C_i

C_i is proportional to the total surface area of the cover, but since the length (l) and width (w) are fixed, the only change is due to small changes in the cross dimension of the spine (that is, the thickness of the paper stack). Thus:

C_i = l(2w + a_i)D_C

where a_i is the “augmented width” of the spine and D_C is the area density of the cover materials (that is, the “GSM weight” of the cover). In conventional specifications, w and l are 9 and 14 cm, respectively, but I will use actual measurements in the calculations below.

Combining these two equations:

W_i = N_iW_S + l(2w + a_i)D_C

Now divide both sides by the area term:

W_i* = N_i* W_S + D_C

where W_i* = W_i/[l(2w + a_i)] and N_i* = N_i/[l(2w + a_i)]. This normalizes the total weight and sheet count of the ith notebook to the “augmented area” of its cover. Notice that each of these normalized parameters, W_i* and N_i*, is defined entirely by known or measurable quantities. Hence, a plot of N_i* vs. W_i* will be linear, with a y-intercept equal to D_C, the “GSM weight” of the cover, and a slope equal to W_S, the weight of a standard sheet in all of the notebooks.

Finally(!), the value of the slope divided by the area of that standard sheet will be the GSM weight of the paper. This is exactly as I described the graphical relationships for the modified standard addition technique, except that the variables are now the normalized sheet-count and weight.

 

Filling in the numbers

Here are the measured or known properties for all four notebooks:

Notebook	Weekly	Wkly/18-mos	Daily	Squared
Ni (sheets)	72	104	200	96
Wi (g)	110	134	223	130
l (mm)	141.5
w (mm)	91.5
ai (mm)	6.74	9.25	17.65	8.95
Total disperson in ai (mm)	0.10	0.23	0.40	0.24

 

The values for the cover dimensions, l and w, are based on multiple micrometer measurements on each notebook. The within- and between-notebook variation is the same at about +/- 0.20 mm around the values given. This presumably reflects manufacturing variation, the “springiness” of the cover materials, and some imprecision and rebound in the adjustment wheel of the micrometer. Absent any reason or result to suggest systematic differences, I have used the same values for all notebooks. The values for a_i, however, are inherently different and were determined individually, with each entry being an average of ten micrometer measurements at different positions around the unbound edges of each notebook. Not surprisingly, the spread of values increases directly with the thickness of the paper stack, from 0.10 mm (72 sheets) to 0.23 mm (104 sheets) to 0.40 mm (200 sheets).

From these, the normalized values W_i* and N_i* can be calculated and the best-fit line determined:

Notice the value of R² (“R-squared”), an unspecified form of correlation coefficient calculated by Excel, which I used to generate the plots. For our purposes, it really doesn’t matter which form it is (Pearson’s, coefficient of determination, etc.), but only that it has an astonishingly large value (a “perfect” fit to the line would be R² = 1). Most scientists will work with values of 0.7 to 0.8 and higher (social scientists with lower values, some times much lower); and there is the occasional 0.90 or above that arises in some kinds of high-precision data. But 0.998 is really exceptional, as good a justification for inferring linear behavior as is likely to occur.

This highly-correlated line supports our initial assumption of identical common properties in the three notebooks — dimensions, cover materials, and paper. If these commonalities are indeed “universal” for this Moleskine product category, then another notebook that appears to match, say, the Squared Notebook, should also fall on the line. It does:

This graph portrays the essence of science:
• make a prediction — the Squared Notebook should fall on the independently-calibrated line;
• do the experiment — make the measurements for that additional notebook; and
• confirm/refute — plot the data (the red square).
This confirmation is as good as it gets (though it should never be called “proof”). So science works in PenWorld, even if in many respects it is an other-worldly place. (Or maybe it’s the denizens of PenWorld who are other-worldly, but never mind.)

 

Calculating the GSM weight of Moleskine paper

Even though I gave the result much farther up the page for the GSM weight (71.0) that comes out of these equations, I want to document the details. The calculation itself is very simple. The area density of the paper (its GSM weight) is given by:

D_P = W_S/A_S

Notice that D_P is an intrinsic property of the paper (P), with units of g/m², whose numerical value we calculate. By contrast, W_S and A_S are extrinsic properties of a particular sheet (S), with units of g and m², respectively, whose numerical values we have measured (or calculated indirectly on the basis of direct measurements). These latter two values would change, of course, as the size of the sheet changes (which is the definition of “extrinsic”).

We know W_S from the slope of the best-fit curve in the graph of N_i* vs. W_i* (two images above): 0.8717 g/sheet. We have only to divide this number by A_S, with the appropriate unit conversion, in order to get D_P. Piece of cake, right? Well, maybe not….

As I discussed way up above, Brian Goulet did this directly. He simply removed a sheet from a Moleskine notebook (the next larger size, 13×21 cm, compared to what we have been discussing); weighed it; measured its dimensions and calculated the area; and divided the two resulting numbers to get the GSM weight: 72 g/m². Only one problem: the sheet he removed was the innermost one of a “nest” of four sheets. In the jargon of bookbinding, such a sheet is a bifolium, several of which are overlaid and then folded together along the vertical dimension to create this taco-shaped “nest,” called a section, gathering, quire (unprinted), or signature (printed). (I’m going to use signature because it is the only one of the four I have ever heard.) Then each signature is sewed along the fold line, and multiple signatures are gathered by gluing or further sewing to make… well, something. At some point I assume a book emerges. (There were probably more steps and names in between, but it all blurred together. Yes, even in PenWorld there is a limit to what a fanatic can endure.)

Anyway, there is a point to all this. The sheets making up the signatures were originally all the same size. But after folding, the gathered signatures were trimmed along the edge (opposite the binding), the result of which is that the length of the sides of each successive bifolium differs from the adjacent one(s). In other words, in a book with trimmed edges, the innermost sheet in a signature has a smaller area than the next one that enwraps it, and so on, until the largest, outermost sheet is reached. So the sheet that Brian removed and measured was the smallest of four that make up a signature in the classic Moleskine notebooks. Although the differences are very, very small, that means he underestimated the area of the average sheet in the notebook; and since that value appears in the denominator of the equation, the resulting value of D_P (72 g/m²) was overestimated, which is consistent with the difference in our results (though surely not a quantitative explanation).

I removed a single signature (for the interval Thu/07/16/12-Wed/09/16/12) from the Weekly Diary/Planner — 18 mos (figuring this would be the least detrimental when I pass all four along to my stepdaughter Allison, who loves Moleskines and is a self-described “pencil gal”). The photo above shows the inner bifolium of this signature overlaid on the outer, with the left-hand edges butted up along a steel bar. (The top edges are intentionally offset enough to allow the dates across each page to be read.) Note that two indications of the size difference are clearly visible: (1) the center crease of the outer (upper) sheet is slightly to the right of the other crease; and (2) the edge of the outer (underlying) sheet can be seen along the lower right extending beyond the inner (overlying) sheet. The slightly out-of-focus image of the digital display of the micrometer opening, set to 1.00 mm, is legible through the magnifier.

The following photo, taken vertically down through the magnifier lens with no change in the arrangement, shows the 1.00-mm opening of the calipers, precisely centered on the right-hand side mismatch between the inner (left) and outer (right) bifolia. The larger, outer sheet extends half the width of the caliper opening, to within my visual acuity, that is, 0.50 mm. That means, assuming linear change from each of the four sheets to the next, that each is 0.167 mm wider than the previous one. Metaphorically, if not literally, a splitting of hairs.

Eventually, I concluded that I was not really making high-precision measurements. The numbers are high-precision, but there were just too many tiny, uncontrolled movements of the sheets, crimped paper from closing the calipers, etc. In the end, I defaulted to repeat measurements with the steel rulers of bifolium width and height, interpolating to the nearest 0.1 mm, with these results for an average sheet:
• width = 176.6 mm
• height = 139.3 mm
• area = 24,600 mm²
I also estimated the loss of area due to the rounded corners (which Brian noted but did not deduct) by simply folding a sheet back on the Squared Notebook, marking the lost area on the underlying 5×5 mm square, and noticing that it was a bit more than half. Call it 15 mm², or 60 mm² for all four corners of the bifolium.

Then for a single sheet (half of a bifolium, or two sides if you are counting “pages”), which was the base variable in the graphs :

A_S = 0.5(24,600 – 60) = 12,270 mm²

So, at long last, here it is:

D_P = W_S/A_S = (slope)/(sheet area)
= 0.8717 (g/sheet)/[12,270 (mm²/sheet)x(10^-6m²/mm²]
= 71.0 g/m²

 

How could there be more?!!!

“Really?”, a querulous voice asks. “After 11 printed pages, what else could there possibly be to say?”

I didn’t believe the voice myself, so I checked: yes, 11 printed pages… so far. (Reminds me of the classic infomercial line: “But wait! What if we gave you two more pages? Now how much would you pay?!”)

In any report of science results for a lay audience, there is always room for more. It’s why quotes or sound bites from, say, a medical researcher always end with the qualifier that more study is needed before promising research becomes clinical treatment. There are always more populations to be sampled, more variables to be controlled, more extrapolations to be checked. Above all, there is the question of assessing whether the original assumptions hold up. We saw this last one above when I wanted to ignore the fact that the covers of the four notebooks could not be identical.

Even that allowance for the “augmented cover” may not go far enough. On the front and back portions of the cover, there is a “sandwich” of at least three layers (from outside to inside) — leatherette fabric, stiff board, and endpaper. But across the spine, there is no board or endpaper. Instead the sandwich appears to be this — fabric, thin liner, air-space (for flexing), glue, and thread. I suspect that another term could be added to the equations to accommodate this complication (though I’m less sure about then being able to solve them analytically), but I haven’t attempted this. Nor have I taken my X-ACTO knife to one of the notebooks to see what the elements of the “sandwich” actually are. Instead, I was satisfied to assume that the difference would be small enough not to justify the effort. Because the board is by far the heaviest component in the whole cover, however, this means that by not accounting for the lighter weight along the spine, I have overestimated the fraction of the total notebook weight that should be attributed to the cover. That means, in turn, that I have underestimated the GSM weight of the paper, which would move my number toward Brian’s. I suspect it wouldn’t be much of a move, perhaps a tenth of a gram or two, but remember my red face on being able to detect the upward curvature of that second graph. We do the experiment for the same reason they play the game.

There are also a bunch of minuscule things that might come into play, for example:
• small fluctuations in paper thickness from one manufacturing batch to another;
• differences in hygroscopic behavior at time of manufacture vs. time of measurement because of changes in temperature and humidity between print shop and lab (read “my desk”); or
• the total amount of ink on the pages of different kinds of notebooks — really.

Ink is real and has mass. So going from plain to ruled to gridded notebooks that are otherwise identical (including number of sheets), the weight must increase because of the increasing amount of ink in the patterns. In principle it should be taken into account, but detecting the change would require a high-precision balance, beyond the respective 0.1-g or 1-g resolution of Brian’s or my little scale. The result would be more places to the right of the decimal point in the GSM weight, but surely no improvement in accuracy. In any case, we can only judge the latter if Moleskine decides to reveal the “official answer.” And coming full circle, that seems to be a forbidden event in PenWorld.