The Value Of Material Things III
News From the Rear-view Mirror:
I’m usually pretty good at noticing anniversaries and milestones, but I have to admit to missing one. Back in August, officially, I posted CM’s 1250th article or part-article, Holistic NPCs: Creating Special Characters, which gave a process for finding consequences and ramifications of character elements that would feed back into other areas of a character’s life.
.
Now, some of those posts were announcements like “No Post Today”, so I try to avoid counting those, so in my book, the “Real” 1250th post was How Long Is A Generation? in mid-September, which tried to bring some order to a particular patch of chaos – the number of possible durations covered by the term “a generation”. I wasn’t entirely sure that I had succeeded, so I changed the subject to work around the question to a practical solution based on family history.Anyway, acknowledgment of the milestone is overdue and this note is intended to remedy that oversight.
News from a new Tomorrow
I haven’t had time to do a lot of looking back over the last couple of months. I’ve been given notice to vacate my existing accommodations, and have been packing and searching for a new home – one that I can afford, which in Australia at the moment, is a very big deal.
I inspected one place over the weekend, and if it had worked out, I would hope to have been migrating by the end of next week – but it didn’t. I have until the 9th of January (if I can’t get an extension) – but there’s a Christmas and New Year in the middle of that time-frame.
I’ve been trying hard not to let it stress me (and succeeding – I think that I’m the calmest and most confident of my family). In fact, the perfect place was on offer a week ago – but by the time I was able to contact the agents, it had already gone.
So the quest continues. 2BR, no yard maintenance, Ground Floor preferred unless there’s a lift, car-park would be nice but I don’t need one, A$395 a week or less, own laundry space, no more than 125m from a bus stop or railway station, preferably in the Canterbury-Bankstown area of Sydney – just in case someone knows of a place!
I expect Campaign Mastery to be disrupted, in terms of new posts, probably with little or no notice. But I’m going to try to post anyway.
So, on with today’s post. Today, I want to talk about valuing an Ebony Statue of Anubis, and then have a whack at principles for valuing a Tapestry. If there’s time, I’ll also talk about paintings, and maybe more, but if not, they can wait for another day.
Valuing An Ebony Statue
Ebony is a rare type of wood. That makes it a renewable resource. Right away, that’s different from just about everything else that this series has talked about.
Or is it? Talking about gems or gold, we may be talking about a finite resource that has to be dug out of the ground, but the bottom line remains, in both cases, that there is just so much of it extracted in a year, and that (plus any leftovers) is all that’s available.
The Value Of Ebony
According to Google, it’s price can exceed $100 per board foot or $10000 per kilogram, and can even go as high as $13000 per cubic meter.
Hearne Hardwooder has more detailed pricing:
- Avg. Weight Per BF: 5.33 lb/ bf
- Rarity: Moderately Rare
- Typical Avg. Width: 3″ to 4″
- typical Avg. Length: 3′ to 5′ “
[Ebony is] “a very dense wood with specific gravity of 1.2, it is usually only available in widths less than 6″ and lengths less than 48”.
Their price list (slightly abbreviated) is:
- Thickness 4/4 Grade Premium Width Range 4″-12″ Length Range 48″-144″ Price per bf $150
- Thickness 4/4 Grade Select & Better Width Range 1″-6″ Length Range 12″-72″ Price per bf $125
- Thickness 4/4 Grade Unselected Width Range 1″-6″ Length Range 12″-72″ Price per bf $100
- Thickness 8/4 Grade Premium Width Range 4″-12″ Length Range 48″-144″ Price per bf $150
- Thickness 8/4 Grade Select & Better Width Range 1″-6″ Length Range 12″-72″ Price per bf $125
- Thickness 8/4 Grade Unselected Width Range 1″-6″ Length Range 12″-72″ Price per bf $100
Specific gravity
1.2 means that it weighs 1.2 times as much as the equivalent volume of water. A cubic meter of water is 1000 kg, so ebony is…
1200 kg / cubic meter
= 1.2 g / cubic cm
= 33.98 kg / cubic ft = 74.913 lb per cubic foot
= 19.6645 g / cubic inch = 0.6936 oz per cubic inch.
Width & Length
Some of that, I understood right away, like the Width Range and Length Range.
Prices
The prices, I assumed to be in US$ and checking their ‘about us’ page, I see the company is based in Pennsylvania, which would seem to confirm that.
Quality
The grading – and differences between grades – I’m not so sure about, but I can make some logical inferences, taking the descriptions at face value – Selected = they hand-pick the very very best, Select & Better = they pick the best but don’t separate out the very very best, Unselected = they just cut it to length and width, no grading at all. So you might get some good stuff but most of it will be of ‘normal quality’.
I don’t know the relative scarcity of the different grades, but the prices give an indication – 100/125 = 80%, 125/150 = 83.33%. So grade 1 is 100% of all ebony, grade 2 is 80% of that (leaving 20% of ‘typical’ quality), and Grade 3 is 83.3% of that 80%, or 66.666% – so 2/3 is top quality, leaving 13 1/3% in the middle.
This range is so small that I suspect we’re talking about imperfections, and not actually a difference in quality of the ebony itself. 20% has noticeable flaws or inclusions, 13 1/3 % – let’s call it 15% for convenience – has minor flaws or inclusions, and the remaining 65% is as good as it gets.
Thickness
There’s the “thickness”. A quick google search confirmed my suspicion – these are the number of quarter inches of thickness, so 4/4 is one inch thick, 8/4 is two inches thick.
Board feet
Which leaves only one real question of board-feet. Specifically, if a board is 12″ long and 2″ thick, is that two board-feet or one?
A quick google search brings the answer: ” A board foot is defined as a piece one inch thick (nominal) by one foot wide (nominal) by one foot long (actual) or its equivalent. For instance a 2 × 6 also equals one board foot for each foot of length.”
So, thickness in inches × width in inches / 12 × length in feet (or in inches / 12) = the number of board feet.
What about that cubic meter price?
In other words, how many board-feet in a cubic meter?
1 m^3 = 39.37 inches × 39.37 inches × 39.37 inches, or 61023.38 cubic inches.
1 board foot = 1″ × 12″/12 × 1 = 1″ × 1 sqr ft = 1″ × 12^2 sqr inches = 144 in^3.
61023.38 / 144 = 423.7735 board feet in a cubic meter.
$13,000 / 423.7735 = $30.6767 per board foot. Hmm, that doesn’t seem very impressive.
But I’ve double-checked the maths, and it’s rock solid so far as I can see.
The $150 per board foot for premium ebony, × 423.7735? That’s $63,566 per cubic meter (and another 2 1/2 cents, but who’s counting?) For just any old ebony at $100 per board foot, $42377.33.
Implications
Ebony is a middle part of the trunk of a particular tree. It is surrounded by what appears to be ordinary wood. What that quoted $13,000 tells me is that there’s no way you’re ever going to find a cubic meter of the stuff. You might find smaller amounts in greater lengths that add up to a cubic meter, but that’s not the same thing.
In fact, if I assume that length in one direction is not a factor and can be 1m, that means that the ratio of the two prices defines the maximum likely cross sectional area of ebony within the tree, in square meters:
13000 / 42377.33 = 0.3067678 square meters = 3067.678 square cm.
area of a circle = pi × r ^2, so this is 31.2486 cm radius, or a diameter of 62.5 cm, or just over 24.6 inches.
To get anything larger than that, you need to actually cut and put multiple pieces of ebony together, then carve them smooth.
But 24.6 inches is a respectable measure. It’s enough for a human-sized figure – if they aren’t overweight and don’t have their arms outstretched like they did in Leonardo’s “Vitruvian Man”. If you want to render that in ebony, you would need to do the arms and maybe the legs as separate pieces and join them to the rest.
So where does that leave us?
Quality is a factor but not a major one. Using only the very best will add 50% to the value of an object. The base value is $100 per board foot, which equates to:
$1200 per cubic foot
$0.69444 per cubic inch
$0.04237733 per cubic cm
$35.31444 per kg
$16.0184 per lb
The Volume of a statue
There are lots of ways to determine the volume of a statue. The simplest one is the Archimedes method: fill a vessel with enough water to fully submerge the object, mark a line, drop the object into the water and make a second mark. Remove the object and see how much water it takes to get from the first mark (you may need to top up) to the second.
Easy! That is – if you happen to have the actual object in front of you.
Take that option away though, so that you are working from an image, and you have to think a little harder.
There’s a “very” precise way, and there’s a very rough-and-ready way.
Precision first, I think.
Precision Volume Estimation
To demonstrate this, I’ve chosen a lovely Anubis statue from Amazon (if you like it, they were on sale the last time I checked, for $30.64 AUD, about US $19.50 (plus shipping) – but they are currently 24% off, so normal would be closer to $25-26 USD, plus shipping. Just click on this link (I will get a small commission).
The image shows the technique: break the ‘statue’ down into basic shapes and then work out the volume of each, filling in any parts that you can’t see.
To the right of the statue, I’ve done such a breakdown, into 14 parts including the base – but some of them have sub-parts. (NB: you might want to open the image in a new window an put it and the article side-by-side to follow along.)
- The ears are a three-sided pyramid that’s been curved, and had one side slightly hollowed out. You can do it as three three-sided solids or simply make allowances. If the entire statue is, say, 20″ high, that’s about 13.6cm as displayed on my laptop*, so each mm of height in the image is 0.147 inches (if you’re in the US, you might need to work in tenths of an inch; I’ll leave working out the scale for you to do). HINT: I have a small sewing tape measure of soft plastic that won’t harm or scratch my screen. Get one.
I measure the ears as 10mm tall, or 1.47″ in the statue. Allowing for the curvature, that’s probably closer to 1.6″. The base looks to be about 1/4 of this, or 0.4″ for both sides of the ear – one we can see, and one on the far side.
The volume of a three-sided pyramid is 1/3 base area times height.
The base area of a pyramid with two sides of 0.4″ is 1/2 the base × the height – and we don’t know either of those. We can’t assume it’s right-angled triangle, either, or that the base is also 0.4″. But we can be confident that if we draw a line through the peak at right angles to the base, that will give a right-angled triangle. The closest I can get to an answer without such speculation is “0.64 = b^2 + 4h^2”.
Again looking at the image, then, I decide yes, the base is going to be about 0.4″, too.
So 0.64 = 0.16 + 4h^2, and 0.48 = 4h^2, and 0.12 = h^2, and h is 0.346″. Which gives a base area of 1/2 × 0.346 × 0.4 = 0.0692 square inches, and that gives a volume of 1/3 × 0.0692 × 1.6 = 0.369 cubic inches. And there are two of them, for a subtotal of 0.738 cubic inches. But now we have to hollow that out a bit on one side – call it maybe 0.7 cubic inches.
* in reality, if i were to use this method, I would use a much larger image – about 5 times this size, or about 3400 pixels height. Here’s what the head looks like at that scale, cropped to fit the columns here at Campaign Mastery:
- The head is basically a box in this statue. We can’t see all of it but it looks to be about 5 × 5 × 7 mm. Adjusting for our scale of ×0.147, that becomes 0.735 × 0.735 × 1.029 inches, which is a volume of 0.556 cubic inches.
- The muzzle is a wedge shape with the front cut off. But if we assume that its two sides are reasonably parallel, we can work out the side area and multiply that by the width. We can even tweak that to allow for the sides to point inward a bit.
Side shape is a trapezoid 4 × 1 × 4 × 2mm. So we average the two sides that are basically parallel – the 1 and the 2 – to get 1.5.
Next we need the height, or the separation between them – we’ve already specified this as 4mm. So the area is 1.5 × 4 mm – which we need to scale: 0.2205 × 0.588 inches, giving a side area of 0.13 square inches.
Now, if it were the full width of the head, we’d use the width of the head of 0.735 inches. To allow for a bit of narrowing, we just cut that down a little – maybe 0.72 inches. Which gives a volume of 0.0936 cubic inches.
- And so on – I won’t show the detailed working fpr the rest. The hair is two more muzzle-wedge shapes (just a bit larger) plus the bit at the back that we can’t see, which is a box.
- The neck is a cylinder that appears to be narrower at one end than the other – but average the area of the two circles and multiply by the height. Note that this only works with a cylinder of perfectly straight sides – if it curves, this trick doesn’t work. You may have to make allowances for that, usually by increasing the length of the fictional ‘sides’.
- The chest area is either a fairly complicated box shape in which no two sides are parallel, though the rear of the shoulders and the flat of the ribs seem close. Bur you can get further with two half cylinders – again, averaging the area of the round cross-sections gives you what you need.
Actually, technically, they should be two ovals, not perfectly round – the front to back is about 1/d of the diameter side-to-side – but I’ll use a circle anyway, and just take 1/3 off the areas.
- The lower torso can also be considered two distorted cylinders. Same method.
- The legs (and don’t forget there are two) can be done as three distorted cylinders – top of the thighs, just above the knees, thickest part of the lower leg, and ankle
- The toes are a box (actually they are more of two wedges with the ends cut of, but not in this statue).The rest of the foot is basically a wedge. A second wedge contains the heel. I’ve drawn the toe-box and first wedge on the right foot (on the left in the image) and the heel wedge on the other. Again, don’t forget there are two of them. But, since that’s not totally clear from words alone, here’s a diagram:
The lower part of the diagram offers more ‘realistic’ approximations of the shape of the toes. Note the large gaps between, especially between big and 2nd toe. This exclusion zone has been arbitrarily declared to be the same as the extra that gets added because the toes (and feet) have large round pads – see side view. The box is a compromise that is close enough for our purposes and a heck of a lot simpler.
And, for anyone who’s thinking “those don’t look very much like feet”:
I should also probably add that these images are being produced extremely quickly, with little of the care and attention they would normally get from me.
- The arms can be as complicated as you want to make them. I don’t want complicated, so I’ve shown a single cylinder, which assumes that for every loss at the front of the elbow, there is a gain of elbow protruding at the back. Not necessarily true in real anatomy but close enough. Similarly, by measuring the circular part of the cylinder at the armpit, it will be a bit over for the shoulder and the bicep and a but under for everything down to the wrist – which I have assumed more or less evens out.
- I’ve done the wrists as two cylinders. Again, the real things would be ellipses and not circles, but they are so small it doesn’t matter much.
- The hands and ankh in the right hand are the next problem. I use a sphere the diameter of the width of the hand for the clenched fist and some sort of wedge shape for a flattened hand. Here, the sphere plus an allowance of the ankh are close enough.
- And the base – a rectangular block.
- Next, you need to total all that up and then subtract something for the gold if it’s a real gold inlay (which it won’t be on this statue example, of course).
- The end result – a very accurate total volume. After a lot of fiddly little work.
Quick-and-dirty Estimation
There’s a much fast, simpler, solution.
- First, scale the image up to a reasonable human height in your mind. Make a note of the height of the statue and your ‘human estimate’ in inches or cm.
- Second, considering the build of the figure, estimate how much a person of that height and shape would weigh.
- Third, get that weight in grams; the result is roughly the volume in cubic centimeters of that person.
- Now we scale the volume back down – multiply the result by the statue height divided by human height, both in the same units of measurement.
So, in this case, allowing a bit for the ears, let’s
1. say he’s about 5’5″ ‘in real life’ (65″) and 20″ in statue height.
2. He’s a bit thin. In fact, the body shape is almost effeminate. So let’s use a 5’5″ female. 107 lb or less is considered unhealthy, while a healthy range is 108-145 lb. I’ll pick 115 lb.
3. 115 lb is 52163.1 grams. So the volume at “full scale” is roughly 52163 cubic cm.
4. Scale that back down: (20/65) = 0.3077; multiply by 52163 = 16050.5551 cubic cm. Round it for convenience to 16000.
How much ebony?
So we have a volume in cubic cm of 16000.
Ebony is worth $0.04237733 per cubic cm, so multiply that by 16000 = $678.03728. Call it $680.
As a bonus, we can state that the statue (without any gold) weighs about 814 g. About 1.8 lbs. I’d estimate that as about the weight of a moderately-large hard-cover book, 350-400 pages – so I’d pick out a representative few and lob them onto the scales until I found one that matched. If the pages are bigger, like they are in most game books, maybe cut that page count to 250-300 pages.
The Value Of A Tapestry
Oh my, where to begin?
Well, what’s a tapestry? To me, it’s a woven depiction of an image or scene. That means that there are three main elements to the valuation – the storytelling element, the Artistry element, and the Woven element.
Under those headings, I identified a total of 15 criteria, and as a working assumption, decided that they were about equal in importance. This completely ignores things like antiquity and celebrity; the assumption (for at least the time being) is that these tapestries are ‘new’.
The value of a score
The actual change in value that each of these variables represent is incredibly important.
Let’s say that each earns a rating out of 10, and that each point in a rating adds 4% to the valuation contribution. That means that each of the 15 (except size) would multiply the base value by something between 1.05 and 1.4.
1.05^14 = ×1.9799.
1.4^14 = ×111.12.
That’s the multiple of the base value of any tapestry according to its size.
- “The Lady and the Unicorn”, from the late 15th century. One tapestry from the series sold for around $40 million in 2013.
- “The Hunt of the Unicorn”, from the late 15th century. Worth several million dollars per tapestry. The exact prices vary depending on the condition.
- “The Apocalypse Tapestry”, from the late 16th century. The entire set is valued at around $25 million. [but no indication as to how many are in the set].
- “The Devonshire Hunting Tapestries”, from the late 16th century. Worth several million dollars for the set. The exact prices vary depending on the condition.
- “The Raphael Cartoons”, from the 16th century. Notably, the original tapestries are lost; hence the value lies in the designs themselves, which are estimated to be worth millions of dollars.
- “The Barberini Tapestries”, from the 17th century. Worth several hundred thousand to several million dollars per tapestry. The exact prices vary depending on the condition.
refinement
Let’s make it (rating-1), so that a minimum rating is worth the base value, and increase the value of the rating to 8% per point. That gives a maximum from any rating of ×1.72.
1.72^14 = ×1983.345.
I realized at the last minute that I may have gone too fast for some readers. +8% × (10-1) = +72% = ×1.72 – all clear?
Hmm. Nearly a 2000-fold increase.
We need some sort of a baseline, a ratio to aim towards, from which I can work backwards.
Baseline
So, I turned to Google. I’d have done so eventually, anyway, just to be sure I hadn’t overlooked anything. The first link that it pulled up told me::
“Antique tapestry is collectible and highly valuable. However, not all tapestry created before the 1920s is valuable. The most significant determinant of value in the tapestry is whether or not it tells a unique story of a historical event.”
— Canonbury Antiques, 5 Ways to Identify and Calculate the Value of Antique Tapestries
They offer up the following as criteria:
1. Uneven Stitching – thread back whenever was inconsistent in thickness and would cause the tapestry to have uneven stitching. Furthermore, an uneven hem indicates production by hand. Apparently, there are fakes out there – who would have guessed?
2. Range of colors – there were only about 20 dyes available before the 1920s for use in tapestries. So there would be fewer colors in a genuine tapestry, and the colors were manually applied, so they would also be uneven.
3. Type Of Thread Used – Linen, Cotton, and Woolen threads are genuine; Polyester and Nylon are not. But I intended to go further, to encompass some of the Asian pieces, adding Silk to the equation.
4. The Signature – artists from the 15th century on usually incorporate their signature into a design. That’s something I hadn’t thought of. It’s usually woven into the bottom corner or the hem.
5. The story behind the design – those are the storytelling elements that I mentioned. They offer some examples: palace tapestries feature royalty involved in decisive battles or other important events. Also, church tapestry had saintly or biblical figures.
But no actual valuations. Back to the search results, then.
Further clues
Value my stuff dot com offers,
“Tapestries & Textiles can range from Flemish tapestries and Far Eastern silks to English Medieval church embroidery and European table covers. Tapestries and textiles were originally a decorative way to keep cold droughts out of large homes or for large homeowners to decorate tall walls and demonstrate their wealth.”
— Value My Stuff, How Are Tapestries Valued
Okay, that acts as confirmation that I was right to expand the scope of materials.
The page then lists the same five criteria given above, in more or less the same order.
Famous Tapestries
The same page then provides a list of famous tapestries and indicate their values, and this I thought significant enough to quote::
Okay, so that adds a new item, but one that naturally goes with antiquity – condition. Again, that’s not something to factor in; we’re still looking for “good as new” condition values.
But this does tell us that a top-of-the-line tapestry, with antiquity and condition taken into account will be worth millions. Those two caveats make the value notes only indirectly relevant, though – for now.
The Antiquity Factor
The one quote I was able to find was a 150-year old tapestry valued at $2200-$2500. I am expecting tapestries to be highly perishable, hence those mentions of “condition” above. That probably means that they will appreciate very quickly for a while, but when that period of quick growth comes to an end, condition worsening more-or-less keeps pace with growth in value, so they would only appreciate very slowly thereafter.
The ‘famous examples – we had some from the 17th century (400-500 years old), some from the 16th century (500-600 years old), and some from the 15th century (600-700 years old). There was nothing from the 14th century, so I’m guessing that 650 years is the ‘break point’ where rapid appreciation ends.
Furthermore, high perishability means that there would be fewer and fewer surviving in good condition, so that would be a primary factor in causing the rapid appreciation in the first place.
Arbitrarily assuming similarity in size and condition across multiple examples, that gives us a ratio over a number of different time scales.
“The Lady and the Unicorn” – late 15th century, so now about 550 years old. To go from $2500 to $40 million in about 400 years gives an appreciation rate of ×1.01888 per year.
“The Hunt of the Unicorn” – same time period, worth “several million per tapestry”. Let’s call it 4 million, to be on the generous side. Appreciation rate of ×1.0130356.
“The Barberini Tapestries”, from the 17th century, worth several hundred thousand to several million each, mostly depending on condition. So let’s take the best, and note that poor condition can cut the value by a factor of 10 or more: “Several” – so let’s use 3 million this time, 17th century so call it 350 years. Appreciation rate to go from 22500 to 3 million in 350 years is ×1.025 per year.
So that gives us three numbers – ×1.013056, ×1.01888, and ×1.025 per year.
Taking size and condition out of the equation
The size of the $22500 tapestry is 3′ 5″ × 4′ 8″, or 41″ × 56″, or 2296 square inches. I’ll use 2300 for convenience. Looking up the others named on Wikipedia and looking for sizes, I get:
“The Lady and the Unicorn” is actually a series of six. Sizes are given for three:
Hearing, 12.1 ft × 9.5 ft = 145.2 × 114 inches = 16552.8 sqr inches;
Sight, 10.2 ft × 10.8 ft = 122.4 × 129.6 inches = 15863.04 sqr inches; and
A Mon Seul Desir, 12.5 ft × 15.2 ft = 150 × 182.4 inches = 27360 sqr inches.
I have no idea which one sold for the $40 million price tag. It might be none of them.
Not only is that a significant variation across the group, it’s a MASSIVE variation from our base. Furthermore, in getting the size of the base, it was established that there was moderate fading of the tapestry – and we’ve already noted that condition can cut the value by a factor of 10 or more. So those early estimates of the appreciation rate are pretty worthless.
I already know that The Hunt of the Unicorn is a set. Wikipedia refers to them as “The Unicorn Tapestries” and states that there are 7 in the set, one only surviving in two separate fragments. No sizes are given for any of them.
And I could find no reference to “The Barberini Tapestries at all.
Condition
“Slight fading” is going to be at the lower end of the impact on the value, I suspect. So let’s increase the value of the 150-year-old tapestry by a factor of 5 to compensate for that – $22500 -> $112500.
Size
If I don’t know which one to use, I’ll average all three of the nominated ones. That gives me 19925.28 sqr inches – call it 20,000 for convenience. Next, let’s assume that size is a linear function – that is, value doesn’t increase faster with bigger size (though it probably does in reality).
20,000 / 2300 = 8.69565 times the size. So we increase the 112500 by that ratio:
$112500 × 8.69565 = $978260.625. Again, let’s round to an easy-to-use $980,000.
Recalculating
So, to go from $980,000 to $40 million in 400 years is an appreciation rate of ×1.009316 per year. Up 0.9316% a year.
(You can see from this why I work with appreciation ‘chunks of time’ larger than a year. Over a 10-year period, that compounds to ×1.097, or +9.7%. Over 20 years, it compounds to ×1.20377) or +20.377%. Over 25 years, it’s ×1.261. These are far more manageable numbers.)
My own work lists the following appreciation rates for a 400-year time-span:
Slow: ×1.0926 – ×1.14429 every 25 years;
Typical: ×1.09385 – ×1.2091 every 25 years;
High: ×1.176245 – ×1.61617 every 25 years. There is also a higher but unstable rate, but that need not bother us.
Comparing 1.261 to these puts the growth securely in the ‘high’ range, as forecast. So, for whatever it’s worth, this is a minor crumb of verification.
In fact, it’s 19.266% of the way through the ‘High’ range, so if it eventually drops to somewhere in the slow range, I would use a value 19.266% of the way through that range – ×1.10256 every 25 years thereafter.
Final appreciation results
We’re talking about ×1.261 every 25 years, declining to a more modest value of ×1.10256 after 550 years of age.
Rewinding the clock
With these results in hand, we can turn back the clock on our “$22500” tapestry (using the adjusted valuation of $980,000) to get a 0-year value per square inch.
$980,000 = b × 1.261 ^ (150/25) = 4.0206 b; b = 980,000 / 4.0206 = 243,745;
divided by the size of the comparison tapestry, to which we adjusted the value to get that $980,000 = $243,746 / 20,000 = $12.1872 per sqr inch, base value – for a tapestry now considered an antique.
How much of a factor are the factors?
But that’s assuming that all the other factors are equal between our slightly-faded $22500 tapestry and “the Lady and the Unicorn” – something I doubt like the dickens.
With nothing else to go on, we’re comparing a fairly anonymous work that has more-or-less survived to one of the very best, ever.
Note that our baseline of $12.1872 per square inch already takes into account an ‘as new’ condition.
Getting a yardstick
My first thought would be to use a basis of 5.5 (i.e. strictly average) for the lesser tapestry, and 9.5’s for the more famous one. But I think that’s being too generous to the lesser work. I’m going to assume an average of 3.5 across all 14 categories.
14 factors, and a difference of 9.5-3.5 = 6 across each, is a total of 84 points extra for the great work over the lesser one..
So we’re back at the question of how much of a difference those 84 points should make.
It might be helpful to rewind the clock and get the value of the famous work after just 150 years. That’ simply a matter of dividing the $40 million value by our appreciation over 400 years (1.261 ^ (400 / 25) = ×40.87356) to get the comparable value to our 112.500. 978,630 is the answer.
Next, we need to take the size out of that comparison – dividing by 8.69565 gives 112,542.5.
Oh dear.
The problem is that the appreciation rate I’m using is based on the assumption of equal ratings. We’re now talking about changing it to take into account a difference in ratings (making it smaller) – but how much smaller?
We need a yardstick (now where have I heard that, before?)
84 points out of 100. Perhaps the better way of looking at it is the ratio of the total scores after all – that’s going to be the same as the ratio between individual scores because we aren’t yet differentiating. 9.5 / 3.5 = 2.714.
Is a ratings gap that large really only worth less than triple the value?
It doesn’t seem big enough. Squaring the value would be a ×7.367 factor – that seems more like it, but maybe still not enough. Cubing it gives ×19.997 – that’s a more respectable value. But actual testing (redacted from the article) shows it to be way too high. I’ll go with the 2.714, because the difference will increase with every 25-year appreciation period.
Out of all this: a methodology
So, each factor gets rated. Some of these ratings are going to be worth more than others, we don’t care about that yet, because we will lower the value of others to compensate. So long as the total is out of 140, everything’s fine.
Add up the scores. Divide by 100. Multiply by the base value per square inch (which needs to be revisited, but worry about that later). Multiply by the number of square inches in the tapestry, and you have the “as new” value. You can then appreciate it for age and slash the value for condition as you see fit to get the “as it stands” value.
Getting the re-visitations out of the way
There are two numbers that need to be corrected to allow for the difference in ratings. The first is our appreciation rate, and the second, our base value per square inch.
Appreciation rate revisited
Appreciation Rate (old) = 1.261 / 25 years.
Basis: $980,000 to $40 million in 400 years.
Ratings adjustment: 3.5 × 14 = 49 / 140 for the ‘$980,000’ tapestry.
Divide by 100 = 0.49.
Divide the value by 0.49 to get 2,000,000.
Ratings adjustment: 9.5 × 14 = 133 / 140 for the $40 million tapestry.
Divide by 100 = 1.33.
Divide the value by 1.33 to get 30,075,188.
Appreciation rate to get from 2 million to 30.075188 million in 400 years = ×1.0068 per year, or +7.01% every 10 years, or +14.514% every 20 years, or ×1.1846 every 25 years. That’s our adjusted and corrected appreciation rate.
I note that this is higher than the maximum “high” rate, putting it into the “dangerous rate of increase” category, and into the second of those, in which there is a small chance of a price correction and a certainty of a rate change. Since we’ve already decided that there will be a rate change into the slow growth rate, that doesn’t seem all that surprising.
Base Value per square inch, revisited
Base Value (old) = $12.1872
Basis: Adjusted value, 150-year tapestry, rewind to year 0 value, divide by the size of the comparison tapestry (20,000 sqr inches) to get the base value.
2,000,000 = b × 1.1846 ^ (150 / 25); b = 723768.4. Divide by 20,000 = $36.19 per sqr inch.
NB: the recalculations show that low ratings will reduce this base value, while high values will increase it.
The Storytelling elements
Let’s start by defining them and then thinking about what adjustments to make to the base “score out of 10”.
Subject
Is the subject matter something that interests people now, not when the tapestry was created? Note that even the fact that “people believed in such, back then” is enough to convey SOME interest in the subject matter – a curiosity value.
Your subject matter might be religious, it might be political, it might be bucolic or pastoral, it might be social (i.e. depicting everyday life at the time), it might be fantastic (including images of dragons, unicorns, etc, in a world in which they are not real). They could depict an adventure story or an epic landscape or an exotic beast.
Appeal
Is the subject matter handled in a way that appeals to the general public? Would you be caught dead with it hanging on your wall? This isn’t about the artistic merit or how pretty the picture is, it’s about the story content of the image, of the scene depicted.
Perhaps the most famous tapestry of all is the Bayeux Tapestry, which
“…is an embroidered cloth nearly 70 meters (230 feet) long and 50 centimeters (20 inches) tall that depicts the events leading up to the Norman Conquest of England in 1066.”
— Wikipedia, Bayeux Tapestry
In a way, that’s a shame, because it sells short the whole reality of Tapestries. Okay, the size is impressive, and the subject gets historians excited because it’s full of depictions of everyday life amongst the lower classes of society, about whom little or nothing was written at the time, but visually, it’s not all that exciting to the common man. Not like “The Hunt For The Unicorn” or “The Lady and the Unicorn”.
If your subject was religious, the Crucifixion or the Last Supper are bold and dramatic events. So is Moses and the Ten Commandments, or the parting of the Red Sea. There are other subjects that would have immediate and broad appeal. Whereas Methuselah was probably not very photogenic at 1,000 years of age. The life of even a well-known patron Saint probably doesn’t get too many people excited, either.
Are the characters who are supposed to be recognizable, going to be identifiable from their actions or surroundings,- or are they generic?
Some images tell a great story within the chosen subject, even if the context is a little threadbare.
Perspective
Perspective is the subtext, intentional or otherwise. If the perspective on a particular royal court is “The King is Good and Noble” and you happen to be an enemy of said King, the perspective is all wrong – unless you are the minority. If the King is a petty tyrant, then making him look Good and Noble is a snow-job, a PR stunt, and one that is likely to have fallen rather flat. Having court jesters in the scene mocking the King transforms it utterly.
With some perspectives, it’s hard to go wrong – “This is a place of beauty” or “tranquility” tend to be fairly universal in their appeal.
Some images are bereft of perspective, an intentional effort to offend no-one. The results can be fairly banal (earning it a low score) or can simply indicate the removal of irrelevancies to focus on the imagery itself (earning it a moderate-to-good score).
Depiction
This is where the artistic merit of a design enters into the description. If the image naturally leads the eye from one part of the story to another, or focuses the view on the critical elements of the scene, it’s a success. In “Hunting The Unicorn”, it’s hard to miss the Unicorn!
One of the problems with the Bayeux Tapestry is that it’s far too big to take in with a single glance. It’s an entire textbook on the times, and if you look at the whole thing at once, the details become so tiny that they get lost.
It falls short in the design elements of the Depiction. The style is also rather crude compared to other tapestries, which fails to endear it to ordinary viewers, who can’t quite see what all the fuss is about; it’s a work that you need to be educated into appreciating, and even then, it’s only intellectual appreciation.
Finally, there’s the Narrative itself. Does the story have a resolution? Is that resolution satisfactory to the viewer, or does it leave them wanting more? The latter is fine if this is one of a series of Tapestries, but not so great if it’s the climax of the series.
Value Scores – Storytelling Elements
That’s 5 of the 14 values, and if you believe what was quoted earlier, the most important five by some margin.
If I were to double the value from 1 per rating out of 10 to 2, that’s 100 of the 140 points total that the system is built on, done. That leaves just 40 to come from the remaining 9. I could, perhaps, spin one of those out from the ratings system, leaving 8 worth 5 apiece, but that seems a little too extreme for me.
But I have the feeling that’s exactly what those extracts were telling me to do.
When you aren’t sure of what you’re doing, examine some alternatives. You may find one that’s exactly right, or that shows that your first thought was correct, after all. I have a sequence of 5 to contemplate – ×1 3/4, ×1 2/3, ×1 1/2, ×1 1/3, ×1 1/4. Each of these reduces the emphasis on Storytelling a bit (but all retain emphasis in that area over the others to at least some degree).
5 × 10 × 1.75 = 87.5.
140 – 87.5 = 52.5.
52.5 / 9 = 5.83333; 52.5 / 8 = 6.5625.
Nope, that’s not it.
5 × 10 × 1.6667 = 83.335.
140 – 83.335 = 56.665.
56.665 / 9 = 6.296111; 56.665 / 8 = 7.083125.
That’s getting closer.
5 × 10 × 1.5 = 75.
140 – 75 = 65.
65 / 9 = 7.222. 65 / 8 = 8.125.
I have the feeling that this may have gone past the sweet spot.
5 × 10 × 1.3333 = 66.65.
140 – 66.65 = 73.35.
73.35 / 9 = 8.15. 73.35 / 8 = 9.16875.
13 vs 9 – definitely past it.
Not even going to calculate this.
The sweet spot seems to be around 80 points in the storytelling department, leaving 60 for the rest.
I can either make it uniform – 80/5 = 16, so times 1.6 – or I can tweak individual settings.
I never turn down a chance to tweak.
Tweak: Subject.
There are so many great subjects out there, it’s really hard to pick a bad one. Maybe dogs playing poker? Some would disagree with even this being on the list (and I happen to like some of these, myself).
I’m going to cut the top score in subject to 4, but award ×2 points for each rating for a total of 8. That leaves 72.
Tweak: Appeal
I’m going to make this a score out of 5, but apply ×4 points for each rating, for a total of 20. That leaves 52.
Tweak: Perspective
As much as this goes over some people’s heads, for those who get it, it becomes vital to their appreciation of whatever they are looking at. It’s like a sitcom where something comedic is happening in the background without the characters in focus even noticing. Rating out of 5, ×4 points, total of 20, leaving 32.
Tweak: Depiction
For all that I would love to rank this more highly, if there’s one that that the Bayeux Tapestry demonstrates amply, it’s that Depiction is not a deal-breaker the way some of the other elements in this category are. Maximum score of 7, no multiplier, leaving 25..
Tweak: Narrative
And so we come to the bottom line. Rating out of 5, and ×5 points, making this the single most important component within the storytelling element.
Storytelling elements are all about Composition. What do you include and what do you leave out, what do you have those components left in actually doing, and how does it all add together to make a story? Kind of like writing an RPG adventure, isn’t it?
Artistry Elements
So you have a shopping list of things to include, and even some notion of how they are going to tie together. The next stage is to design the way these elements will actually look, bearing in mind the compromises that will need to be made for the medium. Everything to this point has been purely intellectual, but now it’s time to show off your artistic chops, if you are the designer/creator of a tapestry.
Let’s hit those sketch pads! This stage of the process is one of design.
Depiction Artistry
Hands up anyone here who’s been a comic-book artist. Only me? Okay. Getting characters to look consistent from one panel to the next is one of the harder things to master. Ditto getting things to look consistent and recognizable.
I once started a comic which told the story of a “stealth shuttle” stealing enemy satellites. Aside from pilots and control panels (which I needed to use to tell the story), and background star-fields, every image was a photocopy of the real deal – perhaps tweaked a little (turn up the toner for a “stealth shuttle”). The shapes from the photographs were sufficiently different that when a friend read the strip in progress, he thought they were two different shuttles, and had trouble putting the plot together.
You see, you’re constantly compromised by the black-and-white nature of comic art. Less so now, perhaps, due to the advent of digital painting and color separation, but until late in the last century, this was a big deal. Anyone can draw a poster – drawing story and continuity and choice of perspective, that’s tough. In fact, it usually took two people collaborating to get it done, a penciller and an inker, and neither could have done it without the other (except by doing his job as well as yours).
The artistic constraints on painting are more flexible, but no less forgiving. But Tapestries really hit the jackpot in the difficulty sweepstakes. The surface texture is three-dimensional to an extent unlike anything else, and changes apparent shape depending on the angle from which you are viewing it.
The very best artisans would use the weave of the cloth to their advantage the way – arguably – Will Eisner (some art samples) and Wally Wood (art sample here and more here, including the image below) – used the limitations of the comics medium to their advantage.
That’s what this criterion is all about – the execution of the art and using the medium to the artist’s advantage.
Recognition
This is very similar to the item already listed under Storytelling Elements but it’s more about visual recognition, not just of the individuals portrayed (if they are meant to be recognizable) but recognition of the story being told,. and of the particular spin that the artist is putting on it.
I have a very vague memory of an animated short film depicting the construction of a big building, maybe even the Empire State Building, but the story was told by the way the angles on the surrounding buildings changed as level after level was assembled and installed.
The changing skyline (and I am NOT sure it was New York City) was one of the two central characters of the narrative, and we never saw the other; instead, we only saw through his eyes. But that snippet of memory has stayed with me since the mid- or late-60s, so it clearly made an impact.
That’s what recognition is all about. It’s recognizing a comic impersonating someone famous for comedic effect, recognizing throwaway cultural references, recognizing famous ‘guest characters’ wandering through the scene (sometimes uncredited), recognizing who is being satirized in a political cartoon and why.
Approval
Now, this is a hard one. If you show 50 people the same image, some of them will love it and some will hate it; getting any great degree of conformity of opinion usually means that there’s been some sort of pre-selection of respondents. There are exceptions – funny cat pictures can get 100% approval, for example.
The more controversial the statement being made by the work, the polarizing it will be. So low approval will not necessarily be a bar to a high value, but it will restrict the market somewhat – those who do like / approve of it are generally willing to pay more because of the controversial nature of the work, which compensates for any loss of value through reduction in potential buyers.
Dynamism
Static images are a lot harder to create than dynamic ones expressing motion – no, wait, that’s not right. I was once told that by someone who was very good at executing poster-type static images but awful at motion. He also excelled at imitating other artists’ styles by eye, a skill that I never acquired.
I have very few memories of him these days, it was a long time ago, but can remember discussing “Bohemian Rhapsody” with him, and Ol’55’s “On The Prowl”, and “Hurricane” and one or two others. Like Will-O-The-Whisps, these characters float into our lives for brief moments, make an unforgettable impression, and then vanish, stage left. One can only hope that the memories you have left behind in your life are positive ones.
This is another attribute that comic books and Tapestries have in common – they both stubbornly resist the strictures of the still image. But the tapestries of yesterday did not have the same repertoire of conventions and tricks that have evolved within the comic book industry as code for certain activities. Their only referents were real life and painters, and the latter had yet to discover the dynamism of the Impressionist movement, so they generally celebrated stillness, too – the only movement was the motion of the eye as it tracked the path created for it by the artist.
But, like a story told in sequential panels on a page, sometimes that can be enough. Making an image or scene as dynamic as the medium and tools of the time permit is Dynamism.
Value Scores – Artistry Elements
With 80 of the total of 140 points already allocated, the first question has to be how many of the remaining 60 will be dedicated to Artistry elements, and how many reserved for Woven Elements, the actual assembly of the Tapestry?
There are only four elements in this category, while there are 4, 5, or 6 in the next, depending on how you count them. That says that only 20 or 30 points should be devoted here, or maybe some intermediate value like 24.
Let’s just work through them and see where we end up.
Value: Depiction Artistry
I think this is arguably the most important Artistry Element. Rating out of 5, and ×2 points, leaving 50.
Value: Recognition.
The Storytelling element equivalent got a 7-point rating and a ×1. I’m going to retroactively change that to a 5, ×1, and give this category exactly the same rating. So 50+2-5 = 47 remaining.
Value: Approval
I’m going to give this a rating out 5, and a ×0. I don’t think it makes one bit of difference to the ultimate value of a tapestry, just on the size of the market and how eagerly a minority will make up the difference.
Value: Dynamism
This is really hard to achieve with a Tapestry, so demanding it is holding Tapestries to a false standard, in a way. And, it has to be said, you either have it or you don’t, there’s no in-between. Anyone breaking new ground in this regard will also score high in other areas. So: a rating from 0 to 1, and a ×7 multiplier – because if you do have it, your work will be ‘arresting” and ‘attention-getting’. That leaves 40 for the final category.
Woven Elements
The final stage of creation, after all the design and preliminaries are complete, is the execution. How well made is the Tapestry? If it’s going to fall apart as soon as you look at it, it won’t retain any value for very long…
Anything relating to the physical construction of the Tapestry belongs somewhere in this category, but not everything warrants a score – with some of these elements, a direct adjustment of either the base or final price might be more appropriate. Which means no points for those items on the list, and all the more for what remains.
Size
Yes, I know I’ve already handled this, by defining a base price per square inch. I thought it important to mention it, anyway – you’ll see why in a moment or two.
Materials
“Linen, Cotton, and Woolen threads are genuine. Polyester and Nylon are…” and at this point I’m going to substitute “Modern” for the more pejorative adjective. Each of these three will have their own set of characteristics – the size of threads, the resilience of the material, how well it takes and holds colors (and that can vary from one combination of material and dye to another), how resistant is is to other staining, changes with age – there are a whole host of important details hanging from this one thread.
But the whole package of traits is so complicated that I’m going to shortcut the whole lot and say that it all works out evenly in terms of value in the end, that what you lose on the swings you regain on the roundabouts.
So, “Is it made of material? Yes? Move on.”.
Silk is best handled by multiplying the price of a length of silk by the cost of the same length of one of the others.
Exotic Materials
Now, matters become more interesting. Besides the weaving of gold, silver, platinum, and copper alloys in metallic thread form into tapestries, other exotic materials might sometimes be used. What of velvet, or leather? What of beads and precious stones?
So, I’m going to simplify all this down to a single question – to what extent does the inclusion of exotic materials, in whole or in part, increase the value of everything except those exotic materials?
That’s a curly one, isn’t it? I can’t for the life of me seeing it have no impact; almost by definition, these are harder to work with and so increase the craftsmanship on display.
I’m going to solve it by cheating outrageously. Exotic materials can have a rating of 0, 1, 2, or 3:
0 = none used; 0 points.
1 = crudely used: -2 points, add 90% of the value of exotic materials to the final total.
2 = expertly used: +4 points, add 100% of the value of exotic materials to the final total.
3 = transcends/transcended the state of the art, adding to both the value of the exotic materials and the value of the Tapestry in which they have been used. +10 points, and add 120% of the value of the exotic materials to the final total.
So, where’s the cheating? I’m not going to count any of the above against the ‘budget cap” of 140 all told. In effect, I’m saying that the default is not to use such materials (because it is), but that rules are made to be broken, and if you break this one well enough, you increase the valuation limit of the Tapestry.
So we still have 40 points to allocate within this suite of elements.
Thread-count
Look, no-one using a hand-loom and not using Silk is going to get anywhere near the modern thread-counts. Egyptian Cotton with a 3,000 thread-count? Not a chance.
A thread count is determined by adding together the number of lengthwise (warp) threads in an inch and the number of width-wise (weft) threads; the total is the thread count of an item. Interestingly, a 400 to 1,000 thread-count is considered the best for linen; it’s softer than lower counts and lighter than higher ones.
Bedlinen Direct advise,
“Basic quality” bedding of linen has a thread count of 132 to 144, “good quality” bedding has a thread count of 180 to 220, “great quality” fabric has a thread count beyond 300, and “excellent quality” linen has a thread count beyond 400″
— Bedlinen Direct, Is thread count 144 good?
But that’s by modern standards, with modern equipment and expectations. More relevant is this information from Ihaworld:
“…jumpsuit, kurtas, dresses and tops in handwoven handspun muslin cotton in single ply of 150 thread count. One of the finest varieties of handspun….”
— Inaworld, Single Ply of 150 thread count Edit (don’t blame me, I didn’t name their page!)
Sewport adds,
“Plain canvas has a thread count between 50 and 100. It consists of rough, wide fibers with a relatively loose weave.”
— Sewport, What is Canvas Fabric: Properties, How its Made and Where
Sealy, one of the most famous manufacturers of mattresses and bedding here in Australia, offers the following table of ideal thread counts on their “Sleep & wellness hub“:
Cotton: 200-400
Egyptian cotton: 300-800
Percale weave: 200-400
Sateen weave: 300-600
Bamboo: 300-500
Linen: 50-140 *
Silk: 17-22 momme
Microfibre: 90-120 GSM
Flannel: 160-190 GSM
Notice the asterisk? They add, “In the case of linen, you may wish to avoid considerations of thread count altogether. As the fibers are heavier, lower thread counts are often preferable as they are likely to be softer and more breathable.”
Wool is a lot more complicated, because it comes in so many thickness. They don’t use Thread count at all in the wool industry, they use “yarn count”, which takes such things into account – but is purely a product of modern technology, which makes consistent production of wool of a particular thickness and grade possible.
So, time to reach for the bottom line to this issue: The higher the thread-count in a Tapestry, the better-woven the material is, and the higher the quality of the Tapestry will be – though size can be used to compensate for a limited thread count.
Don’t expect modern standards. A thread count of 30-100 is maybe the best you will get.
50-60 is a reasonable standard. 75-85 is good, and 85+ is excellent.
Ignore the whole question if you’re dealing with wool or silk.
So:
<40, score 0, multiply the size of the tapestry by thread-count / 50 to get the “comparable” size.
40-50, score 1, multiply the size of the tapestry by thread-count / 50 as above.
50-60 score 1, ×4.
61-75 score 2, ×4.
75-85 score 3, ×5.
85+ score 4, ×5, and use the ‘silk option’ under ‘Materials’ – in other words, treat this as an exotic material.
That’s up to 20 points; of the 40 to be allocated.
You may be wondering why so many? It’s something that I’ve learned as a digital artist: you get a much better image result if your generation process includes the following steps:
1. Use a canvas that’s exactly 2, 3, 4, (or, occasionally, 5) times the final display size in pixels.
2. Use the same factor on the size of any brushes – so to get a 3-pixel-width line, on a 4x scale, you need a 12-pixel brush. I generally aim for lines to be 2 – 2½ pixels in the finished image, 3-4 in a “heavy” line.
3. When the image is finished, flatten all layers into a single image (errors can sometime creep in otherwise).
4. resample down to the intended image size.
5. duplicate the image layer.
6. sharpen the duplicate. Make sure that it’s above the main layer.
7. Reduce the opacity of the duplicate until the image “looks right” at 100% of scale. NB: it may be necessary to ‘break up’ the duplicate and apply different opacity levels to different parts of the image, especially if there’s strong contrast in some parts of it.
8. Flatten and save the image.It sounds like a lot of work, but it usually only takes seconds.
Tapestry-makers are using viewing distance to achieve much the same result. The tighter the weave, the less they need to do so, and the more richly detailed the image that the Tapestry can hold.
Dye
Dye is a subject that could double the length of this article, as hinted at earlier. Let’s avoid all that, if we can.
First, in a fantasy campaign, I have to assume that there are some exotic dyes that don’t exist in the real world. I don’t care if “Kingfisher Cream” is a color or not for the Tapestry-maker; instead, here’s a couple of quick questions to guide you:
Is the color rich and vibrant? Yes, +3 or +6; No, +0; higher for multiple colors, lower for one.
Is the dye used appropriate to the fabric? Yes, +2, No -2, Maybe +0.
Are any of the dyes unusual or exotic? Yes, +2, No, +0.
Total is up to 10 points, leaving 10 more for the final question.
Durability
Tapestries need to be kept at a fixed tension, or the threads can separate. Too high a tension, though, and they will stretch over time. Tapestry makers sometimes sewed weights in the bottom of their work to match their own rules-of-thumb.
Tapestries under glass are better protected from insects – but in medieval times, this might be expensive/impossible. Magic might come to the rescue, though.
Tapestries in a frame are better than Tapestries that aren’t, unless the maker has used the “hidden weights” approach. The very best artisans might incorporate the frame into the design by having it carved to their specifications.
Tapestries need careful cleaning. Sometimes the dyes aren’t all that permanent.
Tapestries that removed from direct sunlight are less likely to fade over time, and will do so more slowly if they do fade.
Rate the protection and durability of the Tapestry out of 5, and apply a ×2 factor.
Out of points, out of categories – all good here!
Wrap-up
In one of David Eddings books, there’s an exchange that goes something along the lines of,
“I didn’t realize you knew so much about tapestries.”
“I know nothing about Tapestries – but neither did that pompous ass. As soon as I mentioned the word, his eyes glazed over, and I knew I could say anything on the subject that came into my head without him challenging it.”
(I’d find the exact quote but the books are packed and buried several boxes deep).
I can only hope that this article hasn’t had the same effect on readers.
Until next time, have fun and look after yourselves (and each other) over the Holiday Season!
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January 15th, 2024 at 3:41 pm
Your volume reduction process when calculating the volume of the statue neglects two of three dimensions. When you scale something down by height you also scale down the width and depth if you want your proportions to remain constant. A 20″ statue of human-like proportions when compared to a 65″ human will have 3% of the volume, not 30%.
January 15th, 2024 at 4:20 pm
Yeah, I thought that was a little odd, but didn’t have enough time to go back through it. Thanks, d!