Creating a circle that goes through three points on your lawn

I get some off-the-wall questions once in a while. Today, I got an off-the-porch question and decided the answer might make a good blog post. I'm probably wrong about that, but here goes.

My friend Dark Laser (I have changed his name to protect his identity) is putting a flower garden in his backyard. He wants the edge of the flower bed to be a circular arc that goes through three points . Those three points have been defined by a higher power. Maybe the higher power is his wife, or maybe it's just cuz of where the house is. I dunno. Below is the drawing that he sent me.  I hope you appreciate his obvious artistic skills.

Before he sent the email, Dark did a little googling and YouTubing. He came up with one answer in a YouTube video, which I show below.

I'm not sure how to interpret an email that asks me a question, and also sends me the answer. I'm not sure what he meant by this juxtaposition of Q & A, but due to my insecurity, I took the email as a challenge. "See if you are as smart as this guy, John!!" I am certainly not going to allow any dufus on YouTube to out-answer me on any dumb old math question!

The MathTuber who answered this question used analytical geometry, which lies between geometry (which is all lemmas and compasses) and algebra (which is all factor this polynomial and take the square root of both sides). But mostly the video is algebra.

Here's my opportunity to show off my brilliance. The abracadabra algebra video is all well and good, but it doesn't completely answer the original Dark question. I mean, how does Dark use this equation? Does he need to go out and buy a huge piece of graph paper to lay on his lawn?!?!?

I chose to forego the algebraic approach and go for a solution that is more along the lines of Euclid and his book Elements. A lot of this ancient text has to do with making constructions of various figures with a pencil, a compass, and a straight edge. But I don't think Dark has these tools, especially not in the size required to lay this out on his lawn. So, I improvised with more appropriate tools: rope and stakes.

(While I am at it, let me take a moment for more self-congratulations. Pure mathematicians are perfectly content with theoretical answers. But I am an applied mathematician, which means that my math isn't happy until it answers a real world problem. You can't get any more practical than building an aesthetically pleasing flower bed!)

Step 1

Put stakes at Points 1 and at Point 2. Make two equal lengths of rope, and tie them together at one end. You don't need the ropes to be red and blue, as in my diagram, but it may help.

Tie the other ends of the ropes to the stakes at Point 1 and to Point 2. Grab the ropes where they join and pull them taut. Place a third stake at that point. This third stake is shown as a blue circle in the drawing below.

To avoid any confusion, I use the word stake in a general sense. If any of the stake positions should happen to be on lawn then a tent stake could meet the purpose. If the point is on a wood porch, then a hefty nail or a bolt could work. If the point is on a cement slab of a porch, then maybe a can of spray paint could be used to mark the point. Or a bathroom plunger? 

Step 2

Shorten the two ropes and repeat the process to locate a position for a fourth stake, as shown below as a second blue circle.

Now the aha! part, which I mention in order to create a sense of making progress. All circles which go through both Point 1 and Point 2 will have a center someplace on the blue dotted line! I hope you are as excited as I am.

A practical comment -- If the lengths of the ropes in Steps 1 and 2 are very close to the same, then the two stakes will be pretty darn close together. This is not such a good thing. This will lead to uncertainty in the angle of the blue dotted line, which will lead to inaccuracy in the position of the final circle.

An even more practical comment -- As I wrote that last comment (the so-called  practical comment), it occured to me that in Step 2, you could have kept the rope the same length, and merely pulled it to a position above Points 1 and 2. Too bad you already went through the process of shortening the ropes.  

Step 3

If you want to get technical on me, Step 3, is really two steps. It's a repeat of Steps 1 and Steps 2, only with different points. Repeat Steps 1 and 2 with Points 2 and 3. You probably will need to stretch the ropes out if you already cut them.

The green dotted line in the drawing below is analogous to the blue dotted line. All circles which go through both Point 2 and Point 3 will have a center someplace on the green dotted line! 

I know some of you may have jumped right ahead to the big climax, but I will state it here for anyone who might not have quote caught the significance: All circles which go through Point 1, Point 2 and Point 3 will have a center at the intersection between the blue dotted line and the green dotted line. Assuming the two dotted lines intersect, and assuming the two dotted lines are not along the same line, we have uniquely defined the center of the circle.

Step 4

A pure mathematician would stop at Step 3, since the point has been theoretically defined. But an applied mathematician, being of a superior breed, would realize that we still need a way to mark that physical intersection point on the porch.

Here is my suggestion. Place a skinny pole at a possible location for the circle center. Move the skinny pole around until it lines up with both of the blue stakes. Then turn your head and line the skinny pole up with the two green stakes. Then go back to the blue stakes to make sure they still line up. This may take several iterations. (My own experience suggests that copious quantities of beer can reduce the number of iterations necessary, not because beer increases your skill level, but because it gives you a more realistic view of just how important the position of the center of the circle is in the grand scheme of things.) Put a nail or a stake or a plunger at the point of intersection. 

If neither nail nor stake nor plunger will work on the porch, then buy another 12 pack and set it next to the intersection point. When a neighbor stops by to see what you're doing, hand him a beer and ask him to sit at the intersection point. The extra beers will keep him from moving.

A comment for those who remembered taking geometry... The task of finding the intersection would have been done with a straight edge. If Dark happens to have a 2 X 4 that is long enough, he could certainly use that to mark the dotted lines. A can of spray paint could serve to make that line indelibly, so the next owners of the house can appreciate the mathematics that went into constructing the flower bed. I haven't looked in Dark's garage lately, but I am guessing that finding a 2 X 4 that is long enough is a tall order. Or a long order. So, we must resort to an iterative procedure which would have been scorned by Euclid. But being scorned by Euclid is not a big deal. We are using non-Euclidean geometry.

Step 5

We're now ready to finish the project. Attach a rope to the nail/stake/plunger/neighbor at the center, and stretch the rope out until it reaches Point 1, Point 2, or Point 3.

Tie a spike to the  rope at that point. Holding the rope taut, move the spike from Point 1 to Point 2 and then on to Point 3, scratching the lawn to indicate the edge of the circle. If you are not skilled in the art of lawn scratching, feel free to tie a can of spray paint to the rope. I suggest a color of paint which is different from that of the grass. Although I show purple in the drawing below, green paint would provide a real good contrast to the color of my lawn.

Step 6

Pull up a lawn chair and finish the beer, content in having accomplished a good day's work.

The allure of tweeny colors

I recently saw an interesting question on Quora about colors that are positioned between the basic colors. Here is the question, and the answer I gave.

Question: “Why are those color hues so intriguing that linger right between two known colors: between blue and gray, between pink and purple, etc.? They keep me captivated with the visual ‘tease’.”

Interesting question! I have seen this before, and my own observations are that these tweeny colors are interesting and either beautiful or ugly because of this. I don’t know if I have the answer to why, but I have one plausible explanation.

Basic fact #1: There is much information compression and loss of information as an image makes its way from the retina to the upper parts of the brain. If I look out on the room before me, and then close my eyes to attempt to remember what is there, I come up sadly short. I won’t remember anywhere near all the objects, or remember much in the way of details about them. I certainly wouldn’t be able to paint a picture from memory (even if I could paint).

Basic fact #2: There is evidence that colors work the same way. When the lower brain tells the upper brain that a car is red, it doesn’t report the exact color coordinates of the color either an an RGB value or a number from a color matching book. According to the theory, it will generally put the color of the car into one of a small number of buckets. There might be eleven buckets, or maybe there are just a few more.

I suspect you may be inclined to disagree with such a small number. Surely there are hundreds or maybe thousands of nameable colors? The small number in the last paragraph comes from an experiment where people were shown a color and moments later asked to pick that color out of a lineup. This experiment showed that our remembrance of a color skews toward a quintessential version of that color family, and there are not hundreds or thousands of color families. A somewhat desaturated blue is remembered as blue. A slightly orange version of yellow is remembered as yellow.

Here is my blog post on the experiment: How well do we remember color?

This explanation is consistent with the way we perceive the world. I look at a car and say that it is red, completely ignoring the fact that one part of the hood is lighter because of the position of the Sun, and the lower door panel is darker because it is partially shaded. In some areas of the car, there is a strong delineation in color, and I can easily choose to be conscious of that. In other places, the change in shade is gradual enough that it is difficult to be consciously aware of it.

Let’s apply this knowledge to your question. Consider looking at a car that is somewhere between blue and gray. I may glance at it once, and my lower brain will decide that the color is in the gray family. I look again, and my lower brain may change its mind and put the color in the blue family when it reports to the higher brain.

If this happens, we have a cognitive dissonance - the upper brain has to deal with two conflicting thoughts: “the car was gray” and “the car is now blue”. This conflict draws our attention to the color, hence it is interesting.

Where did my indigo? (part 1)

I answered a question on Quora recently. I am so proud of my astute answer that I decided to expound on it to make it into a blog post.

The question: What is the true color of indigo?

In today's blog post, I provide the first answer to that question.

Dyeing is a pigment of my imagination

The words dye and pigment are often used interchangeably. Just don't try that in the presence of any colorist. At best, they will roll their eyes and/or laugh at you.

Cool pic of dyes from Alliance Industries

The general term is colorants, something that is used to impart color. Dyes and pigments are two types of colorants.

Dyes are molecules (often organic) that are incorporated into fibers. As a rule of thumb, they are soluble, and we work with them typically in solution, so they are individual molecules. Also generally they require a binder molecule to attach them to whatever we are dyeing. Dyes are most commonly used for dyeing fabric. Dyes need to penetrate into the substrate (e.g. the cloth fibers) in order to become permanent.

Pigments are made from grinding stuff up -- usually non-organic compounds. Since they are ground up, they come in the form of solid particles with lots of molecules clumped together. when used, they are generally suspended in a vehicle that is evaporated when the paint or ink dries. The vehicle might be water (as in latex paints and inkjet inks) or oil (oil-based paints and lithographic ink) or a solvent such as alcohol or toluene (sometimes used in gravure printing ink). Pigments generally coat the substrate rather than becoming incorporated into the substrate.

I expect everyone to use these terms correctly from now on. This will be on the final exam.

Mordant or less?

When I was young, I remember my sister showing me a neat trick. She showed me how to crush the flower buds of a certain flower between my fingers. The flower excreted a gorgeous rich blue fluid. My sister told me that this was a dye used by Native Americans.

Naturally, I was scolded. Maybe my mother was angry because the fluid stained my hands. More likely, she was angry that I stained my clothes. Then again, maybe she scolded me because I was destroying her irises. But, my memory is hazy. Maybe it was a wildflower. And maybe the Native American dye that my sister told me about was beets. I dunno which version is true, but one fact is perfectly clear. It was Nancy's fault. She forced me to get into trouble. This last part will be on the final exam.

This all left me with the impression that dyeing was pretty easy. You find some natural color in the woods or in a field. You crush the plant, dissolve it in water, and then soak your cloth in it.

Indigo dye is almost that easy to use. You just soak the cloth in a solution of the dye, rinse it, and then dry the fabric. Well, maybe that's a simplification, but I think I have the basics of it.

But making the dye is a bit more involved. The indigo plant has pretty pink flowers, but that's not where the dye comes from. Oddly enough, the dye is made from the leaves. These leaves are mashed and then fermented. The gunk left over is then dried and beaten to aerate it, since the process needs oxygen. Then it is left to dry into cakes.

When I first heard this, I was surprised. Who'da ever thunk to ferment leaves? Who'da ever thunk to ferment something and then not drink it? That part boggled my mind. (I'll get back to that in just a bit.)

Getting back to the dye, indigo is odd in the world of dyes. Indigo is called a non-mordant dye, because it does not require a mordant.

Ok, so what's a mordant?

Most dyes do not have a natural affinity for cloth. That is, they don't stick. Cloth is treated with mordants (like alum or tannic acid) so that the dye molecules will stick. The mordant molecules have an affinity for both the cloth and the dye, so they bind dye molecule to cloth by linking the left arm to one and the right arm to the other.

Here is the lesson that will appear on the final exam: Indigo was one of the earliest dyes because of two properties. First, the dye is created naturally in a way that humans could readily see and imitate. Second, the dye did not require pretreatment of the cloth to fix the dye.

Who invented indigo?

Indigo comes from the the indigo plant, specifically from the species of the indigo plants named indigofera tinctoria and indigofera suffruticosa. I called up the ancient Roman historian, Vitruvius, to help answer the question of who invented indigo dye. He told me that "indigo comes from India... where it attaches itself as mud to the foam of the reeds." Hence the name, indigo, which is derived from the Latin word indicum, meaning substance from India.

Now I can understand how someone would have come up with the idea of fermenting indigo leaves. I surmise that someone noticed that the muddy foam on the indigo plant stained fingers and cloth. They then sought to duplicate the natural process, and likely found that they needed a bit of this sticky foam as a starter. Whatever animicula was in the foam -- maybe it was yeast? -- would greedily ingest something in the leaves and go through some sort of chemical reaction that liberates the indigo dye molecules.

A bit of historical pedanticness -- just which Roman historian I spoke with is a matter of disagreement among historians. The quote above is from Ball, p. 201. Another account (Phipps) refers to Pliny, without a fancy quote. Another author, DeBonnet, attributes a similar quote to Dioscorides in 23 BC. I am not really sure who I talked to on the phone. I had spent the whole night sampling my fermented indigo, and ... well...

Marco Polo brought this dye to Europe from his travels in India. Indigo dye became a much desired item for import from India to Europe, first along the Great Silk Road, and then around the Cape of Good Hope. For example, Dutch ships carted nearly 170 tons of the dye from India to Europe in 1631. This factoid will not appear on the final exam.

Cool picture of the indigofera plant, from Phipps, 1832

I pause here to admit to a gap in my personal recollection of world history. I'm a bit surprised that the ancient Greeks had trade routes going with India. Here I thought Marco Polo was the guy who first connected European commerce with Indian commerce. Did I sleep through that day in history class?

So far, the story goes like this: The recipe for making indigo dye from the indigofera plant was devised in India, which became the source of indigo dye in Europe. There are reports of indigo dye in Harappan Civilization in the Indus valley somewhere around the time 2,000 BCE, so this all makes sense.

But that's only part of the story. A clay cuneiform tablet, dating back to 600 or 500 BCE, was found in southern Iraq with the recipe for creating indigo dye.

Tablet housed at the British Museum

This is a bit of a conundrum having to do with the history of indigo. Suppose you were transporting indigo from India to Babylonia. Would you load your camels or rafts or what-have-you with bundles of leaves, or would you load up with cakes of the processed dye? I'm thinking I would go with the more compressed form. Keep up with me now... so if we have an ancient Babylonian tablet, written in ancient Babylonian cuneiform, that was found in the area that was ancient Babylon... and that tablet gives a recipe for turning indigo leaves into indigo dye...

Do you see where I'm going here? Why would a Babylonian go to the trouble of describing he process to manufacture indigo dye to a Babylonian when Babylonians are only receiving shipments of the processed dye???!?

I think that the indigo plant may have been cultivated in ancient Babylon. I think that indigo seeds were transported from India to Mesopotamia at some point before 500 BCE. Then again, maybe the seeds went the other direction at some time before 2,000 BCE?

Here's another indigo sighting from about that same time period. Herodotus (a Greek historian from about 450 BCE) wrote that in Caucasus "They have trees whose leaves possess a most singular property: they beat them to a powder, and then steep them in water; this forms a dye which they paint figures of animals on their garments." Herodotus doesn't actually use the word indigo, but it sure sounds like he was talking about how to make indigo dye. He also doesn't mention India. Strange.

So, now I'm confused about whether the process to manufacture indigo dye actually came from India.

Let's muddy the waters a bit more. In ancient Egypt, mummies were wrapped in linen. The strips of linen were dyed with indigo. This puts the invention of indigo back to around 2,400 BCE, and perhaps earlier. Did the very ancient Egyptians get their indigo from India? Or did the Indians get their indigo from Egypt? Were there even trade routes between these civilizations at that time? Tell me, just where did the indigo?!!??

There are also early reports of indigo dyes being used in the Xinjiang province of China around 1,000 BCE. Were there trade routes between China and India? Here my meager world history completely falls on its face. I done got edicated in 'murica. We don't need no stinking urapean history there.

Earliest occurrences of indigo dye in various regions of the Old World

I look at the map above, and it seems likely to me that indigo dye was developed independently in Egypt and India, and possibly also in China.

But I omitted one last piece of the puzzle. Indigo dyed fabric was found in scraps of cloth in Huaca Prieta, Peru that date back as far as 5800 BCE! I hope you're as excited about that as I am.

My conclusion: a process to extract indigo dye from the indigofera plant was developed independently in multiple places around the globe. That will be on the final exam.


Stay tuned for part 2 of this series of blog posts, where I investigate Isaac Newton and the indigo that he put in our rainbow!

Want to know more about pigments and dyes?
Have a look at a blog post about mauve, Tyrian purple, and magenta.
Or, check out the blog post about the invention of Klein blue.
Or better yet, have a quick read about vermilion and cinnabar.

Bibliography

Ball, Philip, The Bright Earth, Art and the Invention of Color, University of Chicago Press, 2001

Beloe, William, Herodotus, Translated from the Greek, 1814, p. 254
https://books.google.com/books?id=-6sCAAAAYAAJ&pg=PA254&lpg=PA254&dq=herodotus+indigo&source=bl&ots=DyKZWua1TA&sig=ACfU3U3r-EdOPzBCnicfxexVFzz2j0_qFA&hl=en&sa=X&ved=2ahUKEwiinZjvzunjAhUPiqwKHXQsDjMQ6AEwEHoECGIQAQ#v=onepage&q=herodotus%20indigo&f=false

DeBonnet, Maurice, Origin of Paint Pigments, Varnishes, Vehicles, National Painters Magazine, Vol 48, Jan. 1921, page 26.

Finlay, Victoria, The Brilliant History of Color in Art, Getty Publications, 2014

Mattson, Anne, History of Indigo in the Early Modern World,
https://www.lib.umn.edu/bell/tradeproducts/indigo#s5

Nassau, Kurt, The Physics and Chemistry of Color, The Fifteen Causes of Color, John Wiley and Sons, 1983, p. 285

Phipps, John, A series of treatises on the principal products of Bengal, 1832

Splitstoser, Jeffery C., Tom D. Dillehay, Jan Wouters, and Ana Claro, Early pre-Hispanic use of indigo blue in Peru, Science Advances  14 Sep 2016: Vol. 2, no. 9,

St Clair, Kassia, The Secret Lives of Colour, pps. 189 - 192

Wikipedia, Indigo, https://en.wikipedia.org/wiki/Indigo

Wild Color, History of Indigo & Indigo Dyeing,
http://www.wildcolours.co.uk/html/indigo_history.html

The Red Velvet Cake Effect

I recently stumbled upon a video this week where the speaker described experiments where the presence of color tricked participants into tasting flavors that weren't there. The idea seems preposterous. How can flavorless food coloring impart taste?

How Color Affects Taste, Prof. William Lidwell of University of Houston

As odd as this may seem, it must be true. I mean, I found another video on YouTube that makes the same general claim: "Soft drinks that are blue are considered to be more thirst quenching, whereas soft drinks that are pink are considered to be more sugary, even if they're not." There are not one, but two guys who are articulate, sound intelligent, and have the massive funding required to produce a YouTube video on this topic, so who am I to question their veracity?

The Taste of Color, Trace, for DNews

A little googling turned up similar results. For example, two manufacturers of color measurement devices have blog posts on the topic. Here is a quote from the blog post from Konica Minolta:

"In a study published in the Journal of Food Science, researchers found that people confused flavors when a drink did not have the appropriate color. A cherry-flavored drink manipulated to be orange in color was thought to taste like an orange drink, and a cherry drink manipulated to be green in color was thought to taste like lime."
How Color Affects Your Perception of Food

A blog post from HunterLab points to an important distinction between how color affects our expectation of taste and how color affects our perception when we taste. "[We] constantly evaluate foods based on their hue, from checking if the meat is still red to guessing an avocado is ripe when its skin becomes dark green."

The author goes on to say "Color is so powerful that [it] can override what our other senses are telling us to be true, causing us to taste sweetness that isn’t really there, experience flavors that aren’t present."
Examining the Science Behind Color Perception of Food Flavor and Quality

I'm going to invent a name for this phenomenon: The Red Velvet Cake Effect. The rich flavor of red velvet cake is is an olfactory illusion which is caused by the flavorless red food coloring. At least that's what my wife told me. Again, who am I to question?

Ok. Maybe that's not exactly true. The action of an acid (from vinegar or buttermilk) on natural cocoa imparts a red color to this cake, and this acid probably has an effect on the flavor. But pretty much all recipes for red velvet cake also include red food coloring. Why do this? The red food coloring in the cake tricks us into thinking that the cake is richer in flavor. Or maybe the cake really is richer in flavor?

These are not criticisms

Let me preface my next comments -- the comments about the aforementioned videos and blog posts. I don't mean for my comments to be criticism.

The first three of these reports are infotainment -- journalism targeted to inform and entertain. It is not expected that they go into details about how the experiments were performed. There is no talk of qualification of participants, a control group, accounting for the placebo effect, or the statistical relevance of the results. To go into such details would defeat the purpose of entertaining. Who wants to wade through boring details when all they want from the article is a factoid that they can share at the local tavern?

It's a little known fact that Cliff Clavin never actually said this.
It comes from a John the Math Guy blog post on vermillion.

Another shortcoming of the preceding infotainment  (with no criticism implied) is that none of the first three give specific reference to the experiments. Again, I am not being critical, but the articles don't offer a lot of help to the person who is a bit more than just curious. How can they find the technical paper on the topic?

Let me make this clear. I am not criticizing the first three. Infotainment is a great thing, and these are great examples of infotainment. But let's take them for what they are. Suppose you are president of the American Broccoli Growers Association, and I need to decide whether to fund research for a plant geneticist who wants to adjust the cruciferous color so as to make kids go wild about the taste of broccoli. You really need to research beyond the infotainment articles.

I commend the HunterLab article for moving from infotainment into the realm of edutainment. The article educates as well as entertains. There is a clear explanation of what experiments were performed and how they can be interpreted. And the technical papers and experts are identified so an interested reader can go out to find additional details.

But... I wonder if is there some selection bias in the choice of research papers that have been cited? Do other experiments confirm these conclusions? In true John the Math Guy style, I have done a borderline-obsessive amount of digging to get to the true flavor of this question, not colored by any preconceived notions.

Does the color of the food itself change the taste?

I followed the HunterLab link to an actual research paper from 1980. Here is what a quote from that paper:

"Results showed that color masking dramatically decreased flavor identification of fruit-flavored beverages, while atypical colors induced incorrect flavor responses that were characteristically associated with the atypical color. In addition, the color level of beverages had significant effects on their overall acceptability, acceptability of color and of flavor, as well as on flavor intensity."
Effects of Colorants and Flavorants on Identification, Perceived Flavor Intensity, and Hedonic Quality of Fruit‐Flavored Beverages and Cake

Only with a blindfold could Sherlock tell that all the glasses contained prune juice

Here is another research paper demonstrating that the taste of sweet beverages can be "flavored" by color.

"The results of the present experiment corroborate the findings of the previous experiments, demonstrating the influence of color on taste perception"
"... subjects in the present study were moved by the color stimuli to completely misjudge the flavor of the substance being tasted (calling the birch beer such things as "cherry soda" or "cream soda")."
The influence of color on the taste perception of carbonated water preparations

And yet another...
"Both the colour of the cider itself and the colour of the label significantly influenced perceived flavour and hedonic response to the ciders."
Cross-modal influence of colour from product and packaging alters perceived flavour of cider

Oh! I gotta get me some of that Hedonic Response Cider!

The only fruit-flavored beverage that I drink is wine, so I kinda don't care. The HunterLab article anticipated my predilections so they also mentioned a blog post of theirs that talked about color and wine. That second blog post summarized an experiment where researchers tried to trick professional wine tasters by adding flavorless red food coloring to white wines. The deceit was successful.

"A white wine artificially colored red with an odorless dye was olfactory described as a red wine by a panel of 54 tasters. Hence, because of the visual information, the tasters discounted the olfactory information."
The color of odors

My wife's favorite whine is "I want to go to Miami!"

It is a little known fact that olfactory means "relating to the sense of smell."

This was a bit of a disappointment to me, since I know that, all scientific research aside, I prefer red wines! I probably don't like Riesling, but I'm not sure. I've never riesled.

As you may expect, beer is also important to me. And I know that dark beer is way more better than a an icky sickly pale yellow pilsner. But if two beers differ only in color, does my eye convince my tongue and nose that the beer that is richer in color is also richer in flavor? I can't count the number of times that I have lain awake at night pondering that question!

Interestingly, experiments with beer haven't been as conclusive. The quote below is a bit complicated, but here is what I think it says: If someone is a Miller Lite kinda guy, they are more apt to be fooled by a little brown food coloring. I believe this, but only because it fits my preconceived notion that people who drink light beer are less sophisticated than I am.

"When the participants evaluated the expectations and tasting experience of the two different beers ... (pale vs. dark), after tasting, those who preferred pale beers, rated the darker beer as tasting sweeter than those who usually prefer other types of beers, such as dark ones..."
Dark vs light drinks The influence of visual appearance on the consumer's experience of beer

The Lovibond scale is used to assess beer color

One finding of the next experiment (below), is that before the mug comes to my lips, I expect that a beer with a rich brown color will be richer in flavor than a light yellow beer. Well, duh. The important part of this research is that when I actually taste the beer, my palate will not be fooled.

"Dark and pale beers were evaluated both before and after tasting. Importantly, these beers were indistinguishable in terms of their taste/flavor when tasted without any visual cues. The results indicate that the differing visual appearance of the beers led to clear differences in expected taste/flavor. However, after tasting, no differences in flavor ratings were observed, indicating that the expectations based on visual cues did not influence the actual tasting experience."
The Influence of Color on the Consumer's Experience of Beer

So, let's move on to chocolate, another place where I like to brag about my superior tastes. In my opinion, milk chocolate is for the hoi polloi. Having an affinity for dark chocolate shows that you have culture. But, at least according to this research, my false snobbery can be exposed with a little brown food coloring in the outer candy shell of an M&M. And even worse, just calling  the little rabbit pellets dark chocolate will fool me. Really? Am I that easily misled!?!?!? 

"The participants rated brown M&Ms as being significantly more chocolatey than green M&Ms and “dark chocolate”-labeled M&Ms as being significantly more chocolatey than “milk chocolate”-labeled ones."
The Influence of Color and Label Information on Flavor Perception

I like my chocolate just like my used motor oil - dark and flavorful

This sampling of research papers suggests that color can suggest taste, but that might not always be the case.

Does the color of the plate or cup influence the flavor?

I want to investigate a phrase from the cider experiments which I skipped over: "and the colour of the label". The cider house rules apparently extend beyond the color of what goes into your mouth. The effect on flavor of the color of the coffee mug seems to be fairly well researched. And the research seems to be heavily weighted toward verification of the Red Velvet Cake Effect. I have some quotes below.

"The results revealed that the colour of the cup exerted a significant influence on both pre- and post-tasting ratings for all attributes measured."
Cup colour influences consumers' expectations and experience on tasting specialty coffee

"... the coffee was rated as less sweet in the white mug as compared to the transparent and blue mugs."
Does the colour of the mug influence the taste of the coffee?

"The colour of the cup, for instance, has been shown to prime notions of sweetness (e.g., pink cup) or acidity (e.g., yellow or green cup) that may carry over to influence the tasting experience."

"Given that different styles/varieties of specialty coffee have different dominant/desirable qualities (e.g., acidity/sweetness), in the future, the design of coffee cups may need to be customized for different coffee drinking experiences (e.g., origin or roast), much as seen in the world of fine wine (with different glasses for different grape varieties)."
Assessing the influence of the coffee cup on the multisensory tasting experience

Choose your cup wisely, it will affect the taste of the coffee

Seems pretty conclusive that the Red Velvet Cake Effect extends to coffee mugs. But are pastries on plates any different from red velvet chocolate? Apparently so.

"[No] main effects of the plate colour on the evaluations of greasiness, crunchiness, creaminess, and sweetness [of pastries], as well as the hedonic value and purchase intent in stage 1 and stage 2 could be found."
Visual merchandising of pastries in foodscapes: The influence of plate colours on consumers’ flavour expectations and perceptions

But the color of the plate has a clear effect on the sweetness of strawberry mousse.

"Specifically, we investigated the influence of the color (black or white) and shape of the plate on the perception of flavor intensity, sweetness, quality, and liking for identical strawberry mousse desserts.The results demonstrated that while the color of the plate exerted a significant influence on people’s perception of the food, the shape of the plate did not. In particular, when the mousse was served from a white plate, it was perceived as significantly more intense and sweeter, and was also liked more."
Is it the plate or is it the food? Assessing the influence of the color (black or white) and shape of the plate on the perception of the food placed on it

Choose the plate wisely if the dessert is red velvet cake or strawberry mousse,

leave the ugly plates for pastries

I'm not sure what to make of all this. I am getting a bit peckish for dessert, though.

Survey papers

This limited research has led to some conflicting conclusions. I have browsed through a dozen papers and found that most (but not all) confirmed the Red Velvet Cake Effect. I readily admit that my sampling of technical journals on flavor science has not been thorough. Basically, I have only earned my associates degree in Velvet Cake from Google University. In particular, I would expect that my research would be biased in favor of papers that support the surprising results.

It is a little known fact that red food coloring might be made from Hemipterates (the order of true bugs, in the class Insecta) like the cochineal or kermes vermilio, but that Starbucks has pledged to stop using the natural dyes that are made from insects.

To get a better perspective, I will have a look at scholarly review papers.

Charles Spence (from Oxford) is a prolific author on the Red Velvet Cake Effect. (I say this despite the fact that he has not, to my knowledge, used this phrase. I am sure he will start using it when he reads this blog post.) Here are a few of his papers which provide an overview of a little bit of the research that he has reviewed. When I say "a little bit", I mean... well... the first paper has about three pages of references. The second one has 170 references. I should live long enough to read that many research papers.

Does Food Color Influence Taste and Flavor Perception in Humans
On the psychological impact of food colour
Background colour & its impact on food perception & behaviour

Spence (In his paper "Does Food Color...") makes the following statement:

"Does food coloring influence taste and flavor perception in humans? Although researchers have been investigating this important (both on a theoretical and practical level) question for more than 70 years now (see Duncker 1939; Masurovsky 1939; Moir 1936 for early research), an unequivocal answer to the question has not, as yet, been reached."

Ahhh... that explains the confusing results that I found! Then he goes on to burst my bubble.

"That, at least, would seem to be the conclusion drawn by the majority of researchers in the field."

Slicing the onion thinner

When I asked her for the color of the car, she said it was the color of an onion

Anyone who has passed an intermediate level course in "how to lie with statistics" will recognize that the answer you get depends a great deal on the precise phrasing of the question. There are a number of different but related questions that a Red Velvet Cake Effect experiment could address:

1) Does the color of the food influence my expectation of taste before I sample the food?

2) Does the color of the food influence whether I can correctly identify a given food?

3) Does the color of the food influence my assessment of the intensity of the taste of the food (the gustatory effect)?

4) Does the color of the food influence my assessment of the intensity of the flavor of the food (the olfactory effect)?

Wait... Aren't 3) and 4) the same question? Maybe to you and I taste and flavor mean the same thing, but to people who are really into the science of taste and smell, there is a distinction. Taste is the thing that we do with our tongue when we are not sticking out at people we dislike. We can distinguish only five distinct tastes with our tongue: salty, sweet, sour, bitter, and umami (which means something like savory).

I never developed much of a taste for relativity

Flavor, on the other hand, is detected in the nose. To make things even more complicated, this olfactory (smell) component might be administered orthonasally (though the nose, as when someone pretentiously sticks their nose in a wine glass to detect the nose of the wine), or it may be administered retronasally (through the mouth, like when you take a sip of the wine).

The nose of a wine is best sensed in near silhouette conditions
with clouds and mountains in the background.
Pretentiousness is accentuated by an "I forgot to shave for the past four days" beard.  

As an aside, a true oenophile (which is French for priggish wine snob) will tell you that the best way to tell the nose of a wine is to take a sip, spit it out, and then exhale through your nose. This is an example of retronasal olfaction. A true Wisconsinite like myself would be aghast at the thought of spitting out something that contains alcohol.

Now, how did Spence answer the four questions?

Spence summarized one experiment having to do with the first question. British and Taiwanese participants were asked what they expected a colored beverage to taste like. The Brits overwhelmingly (14 out of 20) expected a brown beverage to taste like cola. None of the 15 Taiwanese participants expected a cola taste - grape, mulberry, and cranberry were their choices. So, the answer to the first question is "yes", but the expectation is culturally dependent.

According to Spence, the answer to the second question is unequivocal. Color influences identification of foods.

According to Spence, the experiments that address the third question do not give consistent results. According to me, the combinations (which colors have an effect on which of the four tastes) is confusing.

According to Spence, the answer to the fourth question is clear cut. Color does flavor our sense of flavor.

Charles Spence, Food Scientist

So, I conclude that the two videos and two blog posts mentioned way back at the start of this blog post are pretty decent in their portrayal of the science behind the Red Velvet Cake Effect. They didn't quite catch all the nuances and slightly contradictory results, but we can't expect everyone to produce blog posts that are as long and boring as this one!

If you have read up to this point, I leave you with a well deserved factoid: The flavor and taste of red velvet cake is most likely due (at least in part) to the red food coloring, which might be manufactured from bugs.


Updated June 3, 2019 - In my haste to pat myself on the back for knowing that Umami has moderately recently been acknowledged as a member of the Taste Bud Band, I neglected another key member of the band, Salty Dog. I have corrected the blog accordingly. Thanks to Robin Myers for pointing this out to me. 

What city in Italy is the color magenta named after?

I have asked this question in my color classes, Inevitably, I get no answer, or answers like Rome? Venice? Flagstaff? I then ask some rhetorical questions: "When was the war of 1812?" "Who is buried in Grant's tomb?" "What is the color of a red dress?" and "Who is the greatest color scientist who ever lived?" This will often prompt one of the more adventurous students to take a wild guess at the answer to the magenta question. For the time being, I will keep you in suspense about the answer cuz I got a little story to tell.

Tyrian purple

The story starts around 1600 BCE with a special purple dye that has been made from the rock snail for several millennia. It takes a lot of these snails to dye all your hankies. Like, a lot of snails. Like jillions of the little guys. About a quarter of a million of these mollusks had to be sacrificed to yield one ounce of Tyrian purple dye. As a result the dye was incredibly expensive - it was literally worth more than its weight in gold.

But it was a distinctive color and it was fade resistant, so fabrics dyed with Tyrian purple were prized by people who had more money than they knew what to do with. Purple is thus associated with royalty. This association grew draconian in fourth century Rome, when no one but the emperor would be caught dead wearing Tyrian purple. Literally. The punishment for wearing Tyrian purple was death.

The rock snail (Murex bandaris), and Tyrian purple

The royalty's purple fetish did not return until 1857 with the wife of Napoleon III, the Empress Eugénie de Montijo. She was the fashionista that all of France turned their eyes to. She fixated on purple, which was then available in one dye that was derived from lichen, and another dye called murexide, in homage to the Murex family of mollusks. It was not made from mollusks. We'll get back to that.

The industrial revolution ushered in a new form of affluence -- money and power that was not associated with family lines and land ownership. Entrepreneurs built factories that made stuff that people bought... enter a burgeoning middle class. With that middle class came the need for stuff to buy to show off one's affluenza. Since Kohler had yet to offer the Numi toilet (with Bluetooth and an intuitive touch-screen remote), that need had to be met by fashionable clothes.

Murexide

Now, back to the source of murexide purple, as I promised. Murexide was first derived in the 1830's from the uric acid found in snake droppings. (Please try to avoid snickering at this. It is most unprofessional.) Apparently the commercialization of this was hindered by the unwillingness of snakes to produce sufficient quantities of excrement. It wasn't until the 1850's, when Europe was importing large quantities of the finest Peruvian bird poop (stop it!) for fertilizer, that would-be murexide producers found a source for the raw materials. Calling the raw material guano only enhanced the desirability of murexide.

A hard day's work in the guano mines

The beautiful color was lightfast (it didn't fade in sunlight like many dyes) but it unfortunately lost its color on exposure to the acidic air of urban life.  The burning of coal soured the air. Still, the European taste for purple had been whetted by bird poop. (I consider that last sentence to be my finest contribution to the field of chromo-scatalogical humor. Feel free to snicker at that.)

But all good times must come to an end. Sadly by 1881, books were being written about the end of the Golden Age of Guano in Peru [see Duffield, for example]. I should note that the decline in the guano market was not so much due to dwindling murexide production as it was the availability of cheaper commercial fertilizers that were locally grown. Modern day politicians should take note of the problems with basing an economy on guano.

"Excuse me Math Guy, what does this have to do with magenta?"
"Hang on, I'm getting to that."

Coal tar

I mentioned the burning of coal in connection with the downfall of murexide purple. In an example of "that which taketh away, also giveth", coal was to indirectly lead to the purples that replaced murexide. So, I may seem to be taking a detour to talk about coal, but trust me. It all ties together in the end.

A compound known as coke was being used to fuel the voracious iron smelting operations in England. Coal has lots of impurities, but coke is mostly pure carbon, so it burns faster and hotter than coal. It is manufactured by heating coal in an absence of oxygen. When it is heated, the carbon in the coal cannot burn due to insufficient oxygen. The impurities in the coal exit either as a gas (coal gas) or as a liquid (coal tar).

Coal gas is a mixture of flammable gases such as hydrogen, carbon monoxide, and methane. Around 1800, a fellow by the name of William Murdock hit on the idea of running the coal gas through pipes to places where it could be burned to produce light. In a792, his home in Cornwall was the first house to be lit at night with gas light. Making use of this byproduct of coke production soon became a business in its own right. By 1812 the British parliament chartered the Gas Light and Coke Company of Westminster, London as a utility company to provide coal gas for lighting.

So, a profitable use had been made of coal gas. How about the liquid byproduct? Coal tar (as one might guess from the name) is a thick black liquid -- the kind of thing you just want to dump into the river in order to make it someone else's problem. But it is also an organic chemist's playground, consisting of over 10,000 different chemicals.

Looking forward to a thick, rich cuppa Joe

Over the coming decades, curious chemists extracted a number of interesting organic compounds from coal tar, including naphthalene (1819), anthracine (1832), and in 1834, both phenol and aniline. I'm not going to get into the utility of the first two, but the latter two are relevant to this story because they could be turned into pigments.

In 1842, a process was discovered whereby nitric acid was added to phenol to create a yellow pigment called picric acid. This was a pretty color bu the pigment lacked commercial success since it was neither lightfast nor resistant to washing. It has found much better use as an explosive. And really, who doesn't want an explosive that has a pretty color?

Aniline, on the other hand, led to the development of many important pigments.

"You mean, like magenta?"
"Please be patient. I'm still setting the stage."

Mauve

1856 London. William Henry Perkin was a mere lad of 18 when he started experimenting with aniline in the hope of finding a way to synthesize quinine. Quinine is derived from the bark of the cinchona tree of South America, and was devilishly expense. It is used to treat malaria, and as a result, it is found in the ever-popular drink gin and tonic. British folks in India were known to contract malaria just to get treated with gin and tonics. But a wise man once said that the bark of the cinchona tree is devilishly expensive. Suffice it to say, a cheap alternative to the manufacture of quinine was a worthy goal for the young Perkin.

Two authors have commented on the naivete of Perkin in one of his experiments. Philip Ball has this to say:

[In one experiment] all he obtained was a reddish-brown sludge. Organic chemists quickly become familiar with this type of reaction -- generally it means the reagents have combined to give an unintelligible mess that is best flushed down the sink.

Garfield explains Perkin's naive tenacity this way:

Most chemists, particularly those trained by Hofmann at the Royal College, would have thrown the reddish-brown powder into a rubbish bin, and begun again.

But Perkin inquisitively continued this utter waste of time with aniline and arrived at a fabulous purple. He dyed a piece of silk with the chemical and was delighted by the brilliant color and the fact that it didn't readily fade. The image below shows sample of silk that was dyed by Perkin in 1860, and which now resides at the Smithsonian. Not Perkin; the sample of silk resides there.

Perkin initially dubbed his dye Tyrian purple, but later settled on mauve, which is the French name for the mallow flower. The chemical is also known as aniline purple, aniline violet,  mauveine, chrome violet, indisin, Perkin's violet, purpurin, rosolane, and violein. There is no dearth of invented words in the field of industrial color production.

The mallow flower

The timing couldn't have been better for Perkin. Remember how I cleverly mentioned the Empress Eugénie de Montijo and her purple fetish which was unsated due to the end of The Golden Age of Guano? In 1857, Queen Victoria wore a mauve gown to her daughter's royal wedding. Empress Eugénie expressed her delight that mauve matched the color of her eyes. The craze was so crazy that Punch magazine satirized the outbreak of "mauve measles". 

There is a lot more to Perkin's story, but it's time to move on to explaining how magenta got its name and how this relates to Italy. But first, we will talk about fuchsia.

"Stop teasing me and answer the question!"

"It's not about the destination. It's about the journey."

Fuchsia

Perkin's success with investigating coal tar sparked a fierce competition between colorists (chemists in the science of dyeing) in England, France, and Germany. They reasoned that there must be other brilliant colors hiding in the murky depths of coal tar. This hunch bore fruit of many colors. The general importance of coal tar in the production of dyes can seen by thumbing through Hurst's 126 page volume, A Dictionary of the Coal Tar Colors. That's right. A volume of 126 pages listing dyes made from color tar. A copy of this can be found on the coffee table of any reputable color scientist.

François-Emmanuel Verguin was one of the French competitors, who created aniline red in 1858. His choice for a color name was the euphonious fuchsine, after the fuchsia flower. In England, Edward Chamber Nicholson created the same aniline red in 1860 by a different process and named it rosein or roseine, presumably a rose by any other name.

Aniline red also goes by the name rubin or rubine, but I have not been able to track down the source, other than being derived from the Latin rubeus, meaning red. You got it. Someone called the dye red because it was purple.

Before I answer the original question, about how the color magenta got its name, I would be remiss to talk about fuchsia without pointing out that it is one of the most misspelled of all color names. Nathan Moroney ran an online color naming experiment for years. He had a website that would display some combination of red, green, and blue, and then ask the person to type in a name for the color. The pie chart below shows that there are three misspellings of fuchsia that are more common than the correct spelling: fuschia, fuscia, and fushia. Only 10% of three respondents spelled the word correctly.

But I digress. Let's return to the story, which is already in progress.

The Battle of Magenta

The Battle of Magenta, fought near Magenta, Italy, occurred on June 4th of 1859. This was a decisive battle in the Second Italian War of Independence. The French-Sardinian alliance, led by Napoleon III, won out over the Austrian forces. Yes. This is the same Napoleon III who was mentioned earlier for having a fashionista wife. An interesting coincidence, but unrelated to the question at hand.

The Battle of Magenta, by Gerolamo Induno

I will quote from three sources as to how this battle relates to the newly created dye, aniline red.

Philip Ball offered this explanation:

But the color became more popularly known as magenta, named in honor of the Italian town where the French army fought and defeated the Austrians in June 1859.

Ok... sounds good. But how did the dye get associated with the battle? Kate Smith's rendition:

The Battle of Magenta, fought on the outskirts of the town during the Second Italian War of Independence. Some historians say the Battle of Magenta was a turning point in the war. ... The color reminded someone – most likely the person who named it – of the uniforms worn by the Zouave troops of the French army.

Maybe this is the connection? But it begs the question about what dye was used for these uniforms, since the dye was brand new. And another thing that bothers me: I understand that the image above of the 160 year old painting painting as rendered on my computer display is not likely to be color accurate, but the color of the uniforms seems to be closer to red than magenta.

Victoria Finlay had a more practical take on the matter:

It's first name "fuschine" (from the reddish-purple flower fuschia) was too easy to mispronounce, and it got better sales when renamed after a battle that year in the town of Magenta in northern Italy.

Kassia St Clair has offered an even more business-savvy explanation. I have found no other evidence of her assertion that one of the first sales was to an army, but the explanation is compelling.

The first customers [of the dye], intriguingly, were several European armies, who used it to dye their uniforms. The names, though -- 'fuchsia' in France and 'roseine' in Britain -- would not do for so dashing and assertive a hue. Instead, it became known as 'magenta', in honour of the small Italian town where, on 4 June 1859, the Franco-Piedmontese army won a decisive victory against the Austrians.

So, the connection between the war and the dye is a matter of heated dispute. But one thing is clear. The name magenta was good product branding.

Solferino?

Hurst's Dictionary of the Coal Tar Colours lists one more name for the dye: solferino, but neglects to give a source for the name. I found this a bit confusing. The word reminds me of sulphur, which is yellow. Of course, it also reminds me of the purple sulphur bacteria. It would probably not be a good marketing move to name a sexy new dye after a type of bacteria. I can understand why this name didn't stick.

So, naturally, I started googling. I found out that Solferino is the name of another city in Italy. Oh? Interesting. I dug a bit further. It seems that there was a battle fought in Solferino, 20 days after the Battle of Magenta. Oh??? Isn't that interesting?!?!?!

Simon Garfield offers some explanation. The first time I read his account, I missed the fact that it is talking about two different names for the same color.

In Britain, it [aniline red] became known as solferino and then magenta, taking the names from the Franco-Piedmontese war against Austria and Garibaldi's victory in North Italy, where the dye matched the color of the soldier's tunics. 

Here is a different explanation from an online dictionary

After Solferino, a village in northern Italy, where the Battle of Solferino was fought on June 24, 1859, resulting in forty thousand casualties in a single day. The color was named so because the dye of this color was discovered shortly after the battle, and supposedly the color represented how the battlefield appeared after the bloodshed.

One one trivial correction - the dye was discovered shortly before the battle, not after. Another rather bigger error - blood is red, not fuchsia. Blood dries quickly to a dark brown. I don't find this a credible explanation.


My own best guess is that there was a large order of aniline dyes for military uniforms that occurred slightly after the Battles of Magenta and Solferino. Patriotism and the positive image of a winner became useful branding for the new dyes. Both town names were used, but magenta won out in the end, possibly because of the connotation of solferino with sulphur.

And that, my friends, is how the color magenta got its name.

Bibliography

Ball, Philip, Bright Earth, Art and the Invention of Color, University of Chicago Press, 2001

Blaszczyk, Regina Lee, The Color Revolution, Massachusetts Institute of Technology, 2012, pps. 21 - 44

Duffield, Alexander James, The Prospects of Peru: The End of the Guano Age and a Description Thereof, Newman and Company, 1881

Finlay, Victoria, The Brilliant History of Color in Art, J. Paul Getty Museum, 2014

Garfield, Simon, Mauve, How One Man Invented a Color that Changed the World, Faber and Faber Limited, 2000

Hurst, George H., A Dictionary of the Coal Tar Colours, Heywood and Company, 1892

Lunge, Coal-Tar and Ammonia, Gurney and Jackson, 1882

Meldola, Raphael, Coal and what we get from it: A romance of applied science, 1913

Moroney, Nathan, The many misspellings of fuchsia, from Colour Coded, Society of Dyers and Colourists, 2010

Smith, Kate, Italy | The Colorful City of Magenta,

Smithsonian Libraries, Making Color

St Clair, Kassia, The Secret Lives of Colour, John Murray Publishers, 2016, pps. 162 - 164, 167 - 171

A new color has been patented!

Milwaukee, WI. -- Rufus Chromaphile, spokesperson for John the Math Guy, LLC announced today the issuance of US Patent 10,244,600, assigned to John the Math Guy, LLC for a new color. "This patent represents a great leap forward for fashion, for design,  for art, and most important, for color science. John TheMathGuy has truly demonstrated thinking outside the rainbow on this one!"

When asked to comment, TheMathGuy explained the brilliant Aha! that led to this invention. 

"I was pondering about how it's not possible to stimulate only the M cones in the human eye. If you go to the edge of visible light at the infrared end, you can effectively stimulate only the L cones, and you will see red. If you go to the ultraviolet edge, you can stimulate only the S cones and see a lovely violet. Unfortunately, all visible light which stimulates the M cone (the one in the middle) will also stimulate the L or the S cones. What if we could see a color which only stimulated the M cones?"

TheMathGuy reasoned that he had to use light similar to ultraviolet and infrared to get this effect, but obviously it couldn't be either of them. The Aha! moment came when he started thinking about the compliments of these two colors, ultrared and infraviolet. He rushed to his lab to dig out a darkon generator (which generates anti-photons) and a monochromator (which isolates a single wavelength of light). After a quick trip to American Science and Surplus, he developed a way to combine ultrared and infraviolet.

The resulting color was so mind-blowing that it sent him to the emergency room, but not before he emailed a quick description to his patent attorney. 

The name of this new color? Ubergreen. 

Simulated Ubergreen