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by Béla Lukács

Matter Evolution Subcommittee

H-1525 Bp. 114. Pf. 49., Budapest, Hungary


The problem of the tekhelet (the prescribed colour of the string of the tzitzit) is discussed in a theology-independent way via colour vision theory.


There is a site of Karaites (Karaim) of the Holy Land [1] on Internet; a service for World's Karaites but also a treasury of religious information. That is important, since the Karaite community is not easy to be distinguished from Israelites (called by Karaites Rabbanites) on one hand, and from Christians on the other. Namely, Karaites accept only the Hebrew Bible (in Catholic language the Old Testament in the Jamnia Canon, in scientific jargon MT); neither Talmud, nor the New Testament. So the religion is cca. the biggest common divisor of the two bigger brothers. This may generate interesting theological questions, which I will ignore here as far as possible. However it poses also a nontrivial question about colour vision and colour naming. This will be the topics of the present study.

I must emphasize that the aim of this study is not theology at all. I do not want to take sides about who should wear what. However even theological solutions should be self-consistent, so if the theological question has been settled in any way, colour vision theory, chemistry &c. can help. I know that this sentence is still cryptic; it will be clear some lines below.

Independently of theological considerations, in this study Christianity will be represented by Catholicism, because of two practical points. First, Catholicism (including Roman & Unitus) is ca. as many devotees as all other Christians altogether. Second, the Ur-Text of Old Testament is Septuagint (briefly LXX) for Catholics (and Orthodoxes), so a quite definite text, while the question is not quite clear-cut for Protestants. While they theoretically accept the Hebrew Canon, the name of the old prophet demonstrates that this is not exactly so. The prophet is called by cca. Jeremiah for protestants but rather Yirmeyahu according to (the Masorete scribes of) the Hebrew Canon. Protestants did have a one and half millenium Catholic prehistory. See also App. A.

After the Second Vatican Synod in principle there is no single text of Bible for Catholics: all languages are official which is a language of an episcopal corps which accepted the translation. I do not use the English text, but for practical reasons translate from Magyar ("Hungarian", my first language) and Greek to English. So minor differences to the official English Catholic text are possible, mainly word order & such.


Tzitzit is cca. "fringes"; some textile appendages, of which four should be affixed at the bottom of garment. Moses tells this as Divine Command in Num. (≡4Mos) 15:37-41. The Karaite English translation seems not to contradict to the two other texts, except for the details of the colour, so I repeat it here. The Tetragrammaton is of course translated in many Christian texts as Yahve, Jahve, Jehovah, or The Lord, but this is pure theology. The colour of the fringes is the real problem; here genuine colour names will be in bold italics. So here comes Num. 15:37-41 in the Karaite English [1] (and I reinserted the numbers):

37And YHWH spoke unto Moses saying, 38Speak to the Children of Israel and say to them, And you shall make for yourselves Tzitzit on the corners of your garments for your generations; and you shall place on the Tzitzit of the corner a string of blue. 39And they shall be for you Tzitzit and when you see them and remember the commandments of YHWH and do them you shall not be led astray by your hearts and your eyes which you whore after. 40In order that you remember and do all my commandments and be holy to your God. 41I am YHWH your God who took you out of the land of Egypt to be to you god; I am YHWH your god.

There is really no equivocality about the habit. True, Christians generally regard Num. 15:37-41 as one about the Commandments overwritten by Jesus (see some such in e.g. Paul to the Romans); but even Christians agree that before Jesus the fringes had been obligatory. The disagreement is in the colour of the strings of the fringes (Tzitzit).

The Karaite text [1] summarizes the disagreement with Rabbanites (=Israelites, but not Samaritan-Israelites) by telling that at least some of the strings have to be blue, because the Hebrew Canon mentions Tekhelet, and that is blue. Still Rabbanites use only white strings telling that the (exact recipe of the) die is lost. (To be sure, now a firm claims to be able to produce true tekhelet paint, the situation is rather equivocal.) Now, continue the Karaite site [1], Tekhelet is blue, and the Torah does not state the exact die. "Any die that produces the color blue is sufficient."

Here 2 trivial comments have their proper places. First, Site [1] uses American English, while I have my state exam from Queen's English. Second, of course, Karaites do not accept oral tradition, while they have worked out logical methods to gain maximal information from the written text, which is, I repeat, that of the Jamnia (=Yavne, =Hebrew) Canon. This Canon has been fixed in cca. 150 CE (=AD, but now the PC hyperneutral term is more natural).

Now: is it true that Tekhelet is simply Blue, or there is something more specific in it? My result at the end will be: something in between. It seems that only roughly one half of the possible "blues" are good even according to Karaite philosophy. We shall see the arguments in due course.


The proper Canon of the holy texts for serving God belongs to theology, so this question will not be the topics of a physical discussion. However it seems that 3 ancient and pure textual canons exist for the BCE texts.

1) The Samaritan Text (Sam). It is accepted by cca. 1000 believers. According to historical folklore they may be descendants of the Northern Kingdom (=Israel), who did not accept Joshiah's Reforms (c. 620 BCE). This canon does not contain the books after Joshua, and Joshua is regarded as honoured history. The language is Hebrew, the script is not the present "quadrate" Hebrew (it is nearer to Phoenician), but homomorphic with it. SP does not yet have a full English translation, but it will be included into the discussion.

2) The Hebrew Canon (MT). As told, it was accepted by the Jamnia Theological Institute just before 150 CE (=AD); later, during 1st millenium, the Masoretes elaborated the vocalism, nontrivial in a pure consonantal text. The language is Hebrew.

3) The Septuagint (LXX). The text is Greek Koine, so clearly a translation. Catholic & Orthodox Old Testaments originate from Septuagint, which is older than the Hebrew Canon.

While the previous sentence may surprise some readers, the situation is simple enough. Let us concentrate on the Pentateuch=The 5 Books of Moses. The traditional theology (of any Mosaic religion) told that these 5 books were written by Moses himself. Still, at least Deut. 34,5-12, narrating the death and memory of Moses, cannot have been written by him. We are sure that some parts of the Pentateuch are indeed very old, and surely all the 5 books were ready in the time of King Josiah; but the exact wording is always questionable when texts are copied by hand. We are also sure enough that since 150 CE(=AD) the Hebrew Canon is fixed, and from some later date it is copied letter by letter, because the Canon is supported by "parity checks". (It seems that the greatest Masoretes lived in 10th c.) But also, the Qumran Texts from Ist c. BCE(=BC) and CE(=AD) do show variants, so in that time copying was not yet exact.

Now, as far as we know, the Septuagint was ready at cca. 250 BCE(=BC), for the books in existence then. True, the Aristeas letter telling this is apocryphal (in Catholic sense); but it can be true, and it is logical.

Namely, when establishing the Diadochos Kingdoms after Alexander the Great and the wars, the Holy Land went to the Ptolemaic Kingdom (Alexandria). Later the Syrian Seleucids tried to take it away, but in the 3rd c. BCE it was kept by Egypt. During this time Alexandia accumulated a substantial Jewish (& Samaritan) population. Now, the first two Ptolemies founded the great Library of Alexandria, and it would be difficult to imagine that the Library would not have kept the Greek translation of the Jewish Holy Scriptures. The Aristeas Letter tells just this. In addition the letter states that the translation was correct, because 72 theologicians translated it independently, and all texts agreed. (Hence the name Septuagint.) While this is clearly an exaggeration, we may accept that a team of cca. 72 translators worked. In this case there was no fundamental difference between the Alexandria and Jamnia canonisators; except two points. The Alexandria text was a translation; but from a text 400 years earlier than the Jamnia one. After the translation the vowel-containing and papyrus Alexandria text was more stable than the pure consonantal Palestine texts on hides. The Qumran texts show this: sometimes a Qumranversion is nearer to the Septuagint than to the Jamnia Canon.

While I am definitely not entitled to decide which Canon should be accepted by somebody not Catholic, clearly if somebody believes that we forgot the exact shade of Tekhelet, the Greek translation far back to 3rd century BCE may give some information.


In Num. 15:38 the Septuagint names the colour of the string purple. The Magyar text calls it bíborlila=purplelilac, but this is pleonasm. Purple and lilac both are red+blue, albeit maybe in different ratios.

Now, we have an almost contemporary Greek scientific author about colours, and he is great Aristotle of Stageira itself. He writes twice about colours [2].

De Coloribus, Bekker N°'s 791-799 is of less importance here (and some scholars believe it a work of a disciple). However Bk N° 442a21-25 in Sense and Sensibilia is explicite. Here Aristotle states that 7 fundamental colours exist; but he immediately neglects yellow, as rather similar to white, and tells that white and black are the extremes. Then 4 truly colourful simple and pure colours exist. According to Barnes' very good text [3], which is, however, too modern at this point, the remaining 4 are crimson, violet, leek-green & deep blue.

Now, these are 20th c. Modern English notions. Aristotle writes phoinikun (for violet), halyrgon (for crimson), prasinon (for leek-green) and kyanon (for deep blue), in this, seemingly uninterpretable sequence. However observe that this is as well a 4-colour rough approximation of the colour circle as our medieval system, only the corners differ; and on this circle the sequence is correct.

More physical arguments will follow in due course. Kyanon=cyan may be translated simply blue, and sometimes this is the best translation. However even in Modern colour naming cyan is blue-green (or green-blue, or sky blue), as in CorelDraw palette. The "blue acid" "cyan" (hydrogen cyanid, HCN) is not deep blue, but greenish blue, or, at least sky blue. And there is no doubt that phoinikun is purple. Phoenicians were the inventors of workable dyeing method for purples, based on the purple snail (Purpura lapillus) and Carthage's war flag was red+purple. (Or: scarlet+purple?) Then there is a common 5-degree sequence behind both the Greek and the Modern 4-degreee ones, only with different cornerpoints:














yellow (orange?)















Table 1: Comparison of the Aristotelian & Modern colour systems.

Indeed, additive mixing (from lights) produces bluegreen from green+blue, and purple from blue+red, while subtractive mixing (from paints) produces blue from bluegreen (cyan) + purple (magenta) (and red from purple and yellow).

Now let us go back to Num. 15:38 in the Catholic (Septuagint) text. The string of the fringe must be phoinikun, so cca. purple. And the translators of Septuagint surely were using both Hebrew and Greek. In addition, according to their positions, they must have known the contemporary Israelite religious practice. While we do not know in what extent they were influenced by Lyceum/Peripatos traditions, we do know that the Library itself was under heavy Aristotelian influence (its first director, e.g., being Demetrius of Phalerum, disciple of Aristotle & Theophrastus). In addition, the cardinal colour names were not Aristotle's invention, but rather a wide convention. The translators of Septuagint were separated from On Sense and Sensibilia only by one century; and much nearer in time to the Josiah reform than to Talmud. I do not know if they knew the exact plant/animal which was used for the paint in times prior the Babilonian captivity; but surely they saw and had coloured fringes considered genuine by the religious community.


Modern colour studies, going back to Newton as the fountainhead [4], then to Young [5] and made operative by Maxwell [6], tell us that there are a finite and small numbers of different sensors in the eye; and if two lights excite these in the same extent (caeteris paribus), then our colour impression will be the same. Maxwell determined the number of different sensors as 3, and from experiments he concluded that the sensitivity peaks of them are in the red, green and blue, respectively. Colour photography and colour TV technique are based on Maxwell's results and they work well enough; so we can continue with this, even if there are signals that a (small?) minority of females has one additive receptor (and cca. 1 % of males lacks one).

As for the sensitivity spectra of these 3 receptors, the literature is big enough, but not fully concordant. Recently it seems that genes for both the red and the green receptors have alleles. From blue it is not yet reported. For green this variability is of secondary importance now, since the sensitivity peak is far from tekhelet. For red this is not necessarily true. Some measurements ended with sensitivity curves with a single peak (either at 590 mμ or at 620), but some gave a secondary peak in the blue, about 445 mμ. This may be important in the explanation of the "violet phenomenon".

The shortwave end of the visible spectrum is called generally violet, although I heard other names too. Now, most subjects (but not all!) report the experience that at the blue/violet boundary the colour "starts to redden". Since in the Maxwellian scheme the colour purple (which is not a colour of any monochromatic light, i.e. "not a spectral colour) is the mixture of (comparable quantities of) blue and red, this seems to indicate that very shortwave "blue" excites the eye as middle blue plus a small quantity of red do. If the red receptor has a small secondary maximum at the "blue" end, then it is easy to understand the "violet" phenomenon; if there is no secondary maximum, then the explanation is somewhat difficult. (Again, personal vocabulary varies: purple and magenta are almost interchangeable, but some people use even purple and violet as synonyms, see e.g. [3].)

It seems as if we were ready with the physics. Objects reflect lights according to the properties of their surfaces; the reflected light enters the eye, and there excites cells. These cells contain some paints, whose absorption spectra modify the sensitivities. "Pure colours" are seen if only one receptor is excited; "mixed colours" are seen if two or all three.

Surely the situation is not so simple. First, the situation is not so simple for "pure colours". Second, this viewpoint cannot explain "colour constancy"; the second problem will need another Chapter.

Average Western & Central European males generally tell that there are 4 "pure colours"; or they include also black & white, which are not colours. The 4 about which there is consensus is red, yellow, green and blue. Russians generally divide the "blue" range into two (sinii & goluboi), so in colour names English-Russian translations must be circumspect. Japanese classify blue & green together.

Maybe the Western & Central European consensus comes from the medieval common practice of heraldics. Of heraldic shields only 4 "paints" and 2 "metals" could be used. The proper heraldic language of England is, of course, not English, but a somewhat Anglicised Norman-French, so I give the English translations as well. The two metals are gold & silver, but when painting the shields they are generally substituted with yellow & white paints, and this practice is quite genuine. On one shield two hues of one colour must not be used, and at different manufactures such hues are considered equivalent. So we arrive at 6 heraldic "colours":













Table 2: Colour names of English vs. Heraldic English (Norman).

and removing again black & white, not being true colours, we have got just the four "pure colours". And now let us see the physical boundaries between neighbouring "pure colours". (To be sure, 3 other colours are sometimes used, namely Purpure/Purple for royal majesty, Sanguine/Maroon for battle victories and Tenne/Brown for “natural colour” of wild animals & parts of human body. But the first two are really exceptional, and the last is rather indefinite a colour.)

For the great majority of observers ("trichromats") some monochromatic lights give excellent representations of the "pure colours". E.g. longwave monochromatic lights seem very pure red, at cca. 560 mμ the colour is bright yellow, at cca. 530 mμ it is bright green, and below 480 mμ (until the "violet phenomenon") it is bright blue.

However these "pure colours" are not the 3 primordial lights of Maxwell; e.g. they are 4, not 3. And not all monochromatic lights seem "pure". E.g. about 510 mμ we see bluish green or greenish blue, neither blue nor green.

Mixed colours can belong to two groups. First, there are "saturated mixed colours", which are all the non-pure spectral colours (as e.g. saturated orange or turquoise), plus the saturated purples, and then remain the unsaturated or pastel colours, got from the saturated ones adding white or gray. Again, the purely physical classification is different. Saturated spectral colours can be realised with a monochromatic light of appropriate wavelength, but saturated purples never; they need a monochromatic red plus a monochromatic blue. Pastel lights always need at least 2 monochromatic lights, but sometimes (in the "purple sector") minimally 3.

And the boundaries are somewhat diffuse; in addition there is nothing of physical nature at the boundaries, moreover, we do not know biological phenomena there either.

As for mixing: for one and half centuries we can industrially reproduce "mixed colours". Except for some mixed colours "very spectral", i.e. very near to the colours of monochromatic oranges, yellowgreens and bluegreens (which exception has its explanation of triple overlaps of the sensitivity curves at middle wavelengths) colours of lights can exactly be reproduced by using 3 lights, bright red, green & blue (additive mixing), and colours of paints by mixing three paints (subtractive mixing), which are:









Table 3: Paints of subtractive mixing.

It is easy to understand the difference between additive and subtractive mixing. Paints on white surface primarily absorb wavelengths, so our eye gets what is not absorbed. So mixing two paints we get only such wavelengths, which are not absorbed by either one. Mixing is often visualized by a colour circle, with the pastels inside; Fig. 1 is this scheme, but, as I have stated, the exact borderpoints are arbitrary. The yellow is not convincing, but I used only the Maxwellian additive mixing, so combined the purest red, green and blue of the Figure. It seems they were not pure enough.

Fig. 1: The colour circle of additive mixing of monitors.

Of course, mixing goes even with more than 3 lights or paints, but then the composition is not unique. Using lights of the 4 heraldic colours, e.g., middle orange can be got by mixing cca. equal quantities of red and yellow, or taking cca. 3 part red and 1 part green; blue would make the orange pastel. The same is true for paints.

Newton's original colour circle contained 7 sectors of unequal sizes. He of course used Latin names; the roughly corresponding Modern English names can be seen in Col. 2. Col. 3 gives remarks. But the Classical Latin and Modern English colour naming systems are far from being homomorphic [7].

















Sky blue

See Russian


Deep blue

Rather Lividus




Table 4: Newton’s 7 fundamental colours in Latin, and their English translations.

The aureus = orange equivalence seems strange for us, but correct after Middle Ages. In Classical times it would have been luteus. Newton's 2 blues are the same as in Russian. Classical Latin used cca. 2 dozen simple colour names (e.g. 4 in the red sector), similarly to modern female practice. (But see a novel of Gerrold & Niven [8], where a castaway space discoverer with a translating computer tells his name to the aliens but the computer translates the word using circumscription, so the aliens name him as Purple, because the computer tells "As-A-Shade-Of-Purple-Gray". Sure, the computer misinterpreted the name Asimov as As-A-Mauve. Really, my doctorand originally called some coloured lines on diagram "mauve", but we have then elaborated a common system.

So, Aristotle chooses kyanon & phoinikun, so cyan & magenta as cornerpoints of composition; the same as we choose in subtractive mixing. Then blue is got by mixing 1 part cyan with 1 part magenta. You may try it.

Outside of the purple region totally saturated colours can be produced by monochromatic lights and only by that. Since dampening by gray, darkening by black or diluting by white causes rather trivial changes making recognition only more complicated, for first approach fully saturated colours will do. A seminal article decades old established almost perfect correspondence between wavelength of monochromatic lights and one consistent set of colour names [9]. Colour names are so various (e.g. in textile industry) that a full list of alternative names would be too much to expect here. The idea was to measure colour coordinates and mach colour cards to lights produced via filters transmitting or absorbing more or less ideal bands centered at some wavelengthsl. The minimal bandwidth was 30 mμ, small enough to produce a quasi-monochromatic light.

The colour cards were the standard cards of the US Textile Color Card Assotiation for silk, valid in the time of the article. Of course, some silk colours were less saturated, but it is almost trivial to project a colour from White to the spectral loop. In some case for any reason the match between colour cards and light was unsuccessful for minimal bandwidth; then we give the silk colour for a greater bandwidth centered at the same l, causing a moderate uncertainty.

Wavelength, mm

TCCA silk colour




US Army Ultramarine Blue


US Army Cobalt Blue


Navy 2




Blue Turquoise




Primitive Green






Crayon Green




Spring Green




Nugget Gold


Burnished Straw


Burnt Orange


Terra Cotta


US Army Brick Red


Official US Army Flag Red


Terminal Red

Table 5: Textile colours and almost monochromatic lights; details in the texts.

Match was unsuccessful at the extreme violet (shortwave) end and for the longwave end; silk colours of such lights were not in use then. There I appended not too definite colour names; going farther the colour coordinates do not change too much. You can see that, although colour go into each other in a continuous way, still we can call the colour red in a general sense above 600 mμ, orange around 600, yellow bw. 570 & 590, green bw. 560 & 510. The blue/green border is somewhere at 500 mμ, light blue, caerulus, goluboii or anything is at 490-480 mμ, deep blue, lividus or indigo or sinii bw. 470 & 450, and below that we see a somewhat purplish-like violet.

For purples no monochromatic match is possible, except for the blue end of the purple line (which is violet). In the purple sector we take X part extreme blue and 1-X part extreme red and to this line we project the point of a silk colour. (We do not use here violet as raw material.) The numbers are somewhat approximate because of the somewhat indirect method. Results are as follows.

Part of Blue in Purple



Deep Blue/Indigo


Parma Violet






Dahlia Purple








Ashes of Rose


American Beauty


Vassar Rose



Table 6: As Table 5, but for purples; mutatis mutandis.

So indeed purples of more blue are violet, lavender, lilac &c., those of predominantly red are called as roses (at least on silk gowns), while the half-half purple is similar to a bright saturated plum (or fuchsia).

Sure, the Bible is silent about the exact plant/animal/mineral whose juice is good to paint the fringes. However we know that the name of colour was tekhelet in Classical Hebrew and phoinikun in Classical Greek; and Aristeas in conformity with the whole Alexandrian Israelite community considered the translation correct. Again, I would not go into theological questions, but somebody in Alexandria surely would have been able to detect a mistranslation of colour names.


The distance between 2 colours can be measured, although colours do not exist in the external world. If the unit is the distance between 2 just distinguishable colours, then the metric tensors measured for the members of the “normal trichromat” majority (80-90 %) are almost the same, so the manifold average is really meaningful. Since the average reader is not Riemannian geometer, here comes a very brief explanation.

Take a space (not a space-time; that would result in pseudo-Riemannian geometry), whose points x={xi} are colours. If they are infinitesimally near, say at xdx and xdx, then the distance will be obtained as

(1) ds² = gik(x)dxidxk

where there is automatic summation for any index occurring twice, above and below, but the summation is not to be written (which is called Einstein convention). In fact we cannot distinguish colours too close, but this is only a technical difficulty. Experiments show that for the normal trichromat majority’s 3*3 metric tensors gikthe x dependence is rather complicated. What is interesting, the 3 dimensional colour space is really curved, i.e. one cannot introduce new coordinates in which the metric tensor would be diag{1,1,1}. And while different persons can have very different distinguishing abilities, that means rather only individual constant scalar multiplicating factors in the individual gik’s, and two metric tensors gik(x) and cgik(x) define the same Riemannian geometry [10]. So the Riemannian geometries of the colour spaces are (almost) the same for the overwhelming majority.

So far, so good. One might ask, why the colour space is of 3 dimensions, but then the answer is that most mammals have 2 dimensions (in human term, they see the absolute intensity + see on a shortwave-longwave scale, so blue vs. yellow), but Primates can distinguish also green from red, and this is an evolution. Who knows, after more 20 Mys we shall be even tetrachromats, with a 4-dimensional colour space.

I do not like this argument, since

1) lots of birds are tetrachromats; and

2) two of my woman colleagues are tetrachromats even today. But let us continue.

OK, the space is 3-dimensional, for any reason. But why is the geometry of space non-Euclidean?

Weinberg (not S. but J.) got the answer in 1976 [11]; while I had to append the theory with one more "gauge invariance" [12], the merit of the explanation is solely his. Let us see it with formulae, but only loosely.

There is an interesting character of human colour vision, called colour constancy, which is such a primitive experience that we do not contemplate much about. We see a leaf of a tree a specific shade of green in noontime, and still see (almost) the same shade at well in afternoon. But the light reflected from the leaf has quite different spectral distribution at noon and at late afternoon.

Indeed, colour photography needs a lot of compensating tricks to correct this (e.g. afternoon and at electric light some filters). This shows that the eye itself cannot provide the colour constancy. Maybe it is done by eye and brain together.

The eye has a set of different receptors. Every kind of them possesses a specific sensitivity Ai(x), where x is either the wavelength λ, or the frequency ν, or any appropriate function of one of them. Then the eye can send some vectors of the integrated intensities

(2) vi = òV(x)Ai(x)dx

to the brain, and nothing else.

Indeed, two vectors are possible. Let us write the triviality

(3) V(x) = I(x)R(x)

where V is the reflected light, R is the reflectivity of the surface, and I is the illuminating light.

We cannot observe R(x) directly. However we can observe the integrals of form (2) for I(x) and V(x). Hence the only hopeful task would be to find out the ri's of form (3). But of course,

(4) ri ≠ vi/ii

Still, something approximate can be done. Imagine that all illuminations have the same form, with so many parameters as the range of the vector indices. (For simplicity, 3.) Let us assume that R(x) is similar, moreover than that form survives multiplication & division. Then vi and ii completely determine the parameters ri, so also R.

Now, obviously the forms are compatible with multiplication/division if all the three functions always are exponential, with the sum of 3 terms in the exponent, and the parameters are the coefficients:

(5) (I,R,V)(x) ≈ exp{poPo(x) + p1P1(x) + p2P2(x)}

and then

(6) pi(r) = pi(v) – pi(i)

So colour constancy works if there is a computer in our brain which makes the assumptions. If the assumptions are optimal for the spectral distributions around us, then the colour constancy will be optimal. (Not exact.) Natural selection leads to optimal codes, because individuals with worse assumptions (for, essentially, the basis {Pi(x)}) die out, by eating poisonous fruits more frequently.

Now, the reflectances & illuminations around us are such as they are. E.g. natural illuminations are mainly the solar spectrum (so a Planck spectrum with temperature 5704 K) filtered by the atmosphere. So the colour temperature is <5704 K in morning & afternoon (the low Sun must pass much thicker atmosphere), while if Sun is occluded but other parts of the Blue Sky (in Old Turkish Kök Tängri, see later) are free of overcast, then Tc>5704 K. The question is, what 3-parameter distribution is the best; Weinberg suggested a quadratic basis:

(7) P0(x) = 1, P1(x) = x, P2(x)=x2

Then the approximations would be Gaussian and inverse Gaussian curves; the first ones are not too bad for Sun and for surfaces having one band of reflection, while the inverse Gaussians simulate purples. Also, we are surrounded by lots of important reflectances, some are more important, some are less so. At the end Evolution selects the basis, She knows exactly what & how.

However there is another task as well for Evolution: our receptors in the eyes can yield better or worse raw data for the brain. Weinberg has shown that, if the basis is fixed, colour constancy/discrimination is best with

(8) Ai(x) = C(x)Pi(x)

If so, then colour vision is determined by 4 functions of wavelength (or anything else): the 3 basic functions Pi(x) and the C(x).

Now came I, telling that illumination I(x) and reflected light V(x) are indeed distributions, but R(x)=V(x)/I(x) is not. If we transform x to x'=x'(x), I(x) and V(x) change accordingly, but r(x) is invariant. So we must not assume the same forms for all three; rather

(9) (I,V)(x) » W(x)exp{prPr(x)}

(10) R(x) » exp{prPr(x)}

So there is a fifth function, W(x), which surely is near to the solar spectrum (Planck). All other results remain unchanged.

But then there is a function H(pi) of the 3 coefficients:

(11) H(p) = òW(x)C(x)exp(prPr(x)dx

so that the metric in the space of the parameters {pi} is

(12) gik(p) = H(p)-12H/∂pi∂pk

Therefore Pi(x), C(x) and W(x) completely determine the metrics. If it is non-Euclidean, it is non-Euclidean because the distributions around us are such that gik is rather not to be Euclidean.

And now let us see some numbers. How many different reds (yellows, &c.) can be seen if the total intensity is the same? The answer will not be unequivical because

1) some observers distinguish better, some worse; and

2) there are transitional colours between "pure" ones, and the boundaries are ill-defined. Still, some approximate average numbers can be given, and here I used [13]. I give here in the respective ranges, the number of the distinguishable saturated hues in the range, and the number of the pastel steps between the most saturated hue and white. So


Range, mμ

N° of saturated hues

N° of pastel steps





















Table 7: Colour discrimination/metrics.

So even the red sector contains ~1000 well distinguishable hues, so we might invent fancy words for a dozen reds; and just this is done by women & textile engineers. And there is no physical law to draw the border of Red and Orange, or that of Cherry Red and Flame Red.

The most colourful sector is Blue, with at least 8,000 distinguishable hues; no surprise that Russian even does not have a common word for blue. However blue is rather ignored by hunters & gatherers ([14]); and as we see, High Feudalism just after 1000 AD still was quite happy with one blue class of colours.

And now we see that indeed there is a rather large range to look for tekhelet.

Fig. 2: Colour circle & colour systems.

Fig. 2 summarizes the problem. It shows a colour wheel, closing in the purple region, where I chose some important points. Of course, the exact choice is somewhat subjective. Also, I am not satisfied with the greenish blue domains, maybe there the monitor paints are not optimal. (Note that the monitor lights are not monochromatic, so not fully saturated.) Anyways, let us see the spokes of the wheel. Starting from purple to red the first stop was: half purple + half red. (I used additive mixing.) This colour I call here Scarlet, Sc, but some people may call it Crimson, or Blood-colour or such. The next stop is Red, R; I manufactured it as pure Red of an old PaintBrush version (which is old, but exactly linearly additive using a checkboard pattern of lights). The next is Orange, O, half the Red and half of a bright Yellow. Then comes the Yellow of the palette, Y, which is now not half Red + half Green of the palette (as was on Fig. 1, where it was not a bright Yellow but rather Grayish Yellow or Yellow Ochre; again a strictly technical problem about not quite saturated TV colours), but some better Yellow of PaintBrush. Then comes Yellow-Green, YG, or Golden Green, or anything (this is the Japanese Midori), half of our Yellow and half of our Green. Next is a bright Green, G, more or less a Grass Green or Leaf Green. The next is Blue-Green, BG, half of our Green and half of a Deep Blue of the palette. This colour turned out to be somewhat dull & dark, I do not know why. But if your computer codes produce nice Turquoise or Cyan, you can substitute that (in your mind). The next step is Sky Blue, SB, which I manufactured as one quarter of Green and three quarters of Deep Blue of the PaintBrush palette. The next is Deep Blue, DB, the bluest blue of the palette. Then comes Violet, V, which is now half Deep Blue and half Purple. Finally the wheel is ready with a bright Purple of the palette.

I am well aware that names of neighbouring hues not always mean the same for different persons, and definitely not in the "red" and "deep blue" sectors. The reasons behind are nontrivial. But one of them is surely the emotional charge of reds (blood, life &c.). Red ochre was used sporadically already in Middle Palaeolithe, and while we cannot exactly tell why, surely it was important. Even now lots of verbal tools use red hues. E.g. in English scarlet is not simply a hue: it can be applied as more or less a synonyme for "harlot", and the Anglicans & Puritans sometimes refer the Catholic Church as The Scarlet Woman, a derisive but slightly less impolite term than The Babylonian Harlot. Both terms go back to Revelations, which book is taken seriously also by the Roman Catholics, who interpret the scarlet beast and his harlot reader in scarlet & purple as the pagan Rome; a natural enough interpretation for 1st c. CE. Anyway, because of the centuries-old polemy and slander it is difficult to use these names of reddish hues objectively. So here I define my language, in connection with Fig. 2.

As I told, I restrict myself to saturated hues. Then take "the ideal red". The physical question of the existence of such a unique ideal red goes to Appendix C; however now we are on the colour circle. A circle does not have beginning or end; it is compactified as 6 of the 10 dimensions of World in supergravity. Now take a red bright and saturated enough, and call this Red0. Remaining with saturated colours, you must not add white or black, and total luminance is trivial, so you can add only Yellow or Blue (or Purple), as you can see on Fig. 2. Now take hues to the Yellow and the Blue directions, not just the first distinguishable neighbours but the two which already differ "substantially", but are still "predominantly Red". They are Red+ & Red-. One is towards "Flame Red", albeit perhaps not yet exactly there, while in the other we can see a trace of Blue, making it exotic or piquant, since the mutual occurrence of the warmest and the coldest colours causes ambiguity. (Also this has something to do with the "Blood Colour", but that will be Appendix D, and venal and arterial bloods definitely differ in the amount of blue component.)

Now here I deliberately selected the following terms of speech:

Red+ = Vermillion

Red0 = Red

Red- = Scarlet

It is told that Vermillion is the colour of the mineral Cinnabar, a mercury complex HgS. As a mineral it is the cinnabarit. (Do not confuse it with HgO, which exists in two forms, a brick red and an orange, but never vermillion.)

I checked this terminology with some colleagues, and the result was more supportive than not, but not unequivocal. The most dangerous point is Scarlet. Some vocabularies tell that Scarlet contains some Yellow; and the coats of English soldiers may have had. Still the emotional connotations imply rather a bluish tint. The femme fatale has rouge and nail polish of colour not the warm vermilion or flame red (that warmness would belong to mothers, sisters or the girl of the next door), but something bloody/"cold”red. "Her mouth as a bloody wound...". Soldiers are also connected with blood, and blood never is meant to have a yellow component. And a harlot is not connected with warmness. So if scarlet is indeed yellowish red, it is a mistake which should be corrected at the other end. But just for this study the cheapest solution is to push the startpoint so that it is between vermillion & scarlet, anything you believe to be scarlet.

Well, you may believe that this is a lazy approach, since e.g. Wikipedia definitely gives the names for some RGB colour coordinates. Then indeed it seems easy to ask, what combination is vermilion, carmine, scarlet, crimson or anything, and it is easy to see that that Scarlet still contains some Green (so Yellow), albeit less than Vermilion, while Carmine does not. Second, if Vermilion is the HgS cinnabarit, then it seems straightforward to ask: which RGB coordinates match cinnabarit. Now, this question has no real meaning/sense, so I answer: none. (At least, for monitor lights.)

Namely, colours do belong not to the reflected spectrum, but to the reflecting surface, in the sense of eqs. (3-10), otherwise colours would very strongly depend on illuminations, while they depend on it fairly weakly. (Colour constancy.)

Now, cinnabarit is a reflectant, so it does have some colour; we should compare HgS with other reflectants as the louse (coccidea) Kermes vermilio, the rouge of a femme fatale, a red coat of an English foot soldier & such to make the sequence from yellowish red to bluish one. But monitor lights are not reflectants. Cinnabarit gives a reflected light matching one triad of RGB coordinates in full noon sunlight, another in the laboratory, and so on. So: RGB coordinates under what circumstances?

And if one sees the cinnabarit in lab neonlight (no colour temperature at all), Kermes vermillio in broad sunlight (Tc=5704 K), and the Scarlet Woman in midnight in a night club (Tc=2800 K), then what?

I will reconsider my language if I get much enough protests. This 3 colour names are rather relative here.

As for the "deep blues", Limiting Blue does not exist physically, so there the "ideal" is surely subjective, because of the "violet mystery" (see Appendix C). For the present my language is that Violet is the colour existing in the rainbow. They are physically not mixtures, while in the language of colour circles they already contain some Red. So the Violet/Purple boundary is physically objective, while the transition is gradual in colour impressions.

Anyway, the reproducible representation would be monochromatic lights with definite wavelength steps from Red (or Scarlet) to Violet, and some mixtures of extreme longwave and extreme shortwave lights in the purple region, but this is impossible by computer software & hardware. In App. E we shall see, why.

This means 11 distinct colours on Fig. 2, and that is practically enough now. The wheel shows only the most saturated colours (which are technically possible); pastels are now omitted. They are within the wheel.

Clearly most languages do not use simple names for all 11 colours; even Ref. [15] stops at 6 (their other 5 are "pastels": white, black, brown, pink & gray). It is just that is interesting, which ones are selected in a specific system as "pure", or "fundamental". This is just the point which we do not know for Old Hebrew, the form of the direct ancestor of Modern Hebrew, in the time of the formulation of the present form of 4Moses. Surely, the book existed substantially in its present form in the time of King Josiah, so about BCE 600, and the colour name tekhelet might go back even to the life of Moses himself. However fine details of a hue may change on a spoken language in 3000 years. So our first 3 examples will be historical.

Aristotle, about 330 BC mentions 5 fundamental true colours. They are: xanthon, prasinon, kyanon, halyrgon & phoinikun. Fig. 2 visualises them as Y, G, BG, R & P, although from the Latin we may guess even a YG behind prasinon and xanthon may or may not have had a partly orange hue as well. As for kyanon, cyan is generally not for a deep blue in modern contexts, and for printer paints Cyan is a Blue-Green, halfway between Green and Blue.

The next extinct language is Latin; the language is extinct, but extremely well documented. I used a dictionary stating that it contains the words of Caesar, Cicero, Curtius, Livius, Nepos, Pliny the Minor, Sallusty, Tacitus, Catullus, Horace, Lucretius, Ovidius, Plautus, Phaedrus, Propertius, Terentius, Tibullus & Virgil [16]. That seems quite enough for us, and surely we do understand even the fine details in the works of these authors; but I appended the colour names from another dictionary with prasinus; that dictionary tells it to be yellowgreen, and clearly it is not independent of Classical Greek prasinon. The names are: ruber, rutilus, luteus, gilvus, prasinus, viridis, glaucus, caeruleus, lividus & purpureus, and they seem to correspond more or less to Sc, R, O, Y, YG, G, BG, SB, DB & P, although lividus=plum-colour may be V as well [7].

Heraldics, just after 1000 AD is simple enough. There are 4+1 coloured tinctures, which may be represented by R, Y, G, B, and P, and details are irrelevant (middle hues must not be used). Observe that if one wants, any of SB, DB or V can be used for Blue, but only one on one escutheon.

Modern English seems to possess the same structure, but Modern Magyar does as well; more or less. Also Modern French &c., albeit Modern Italian seems to distinguish two Blues, azzurro & blu.

Modern Russian is another system, but there Heraldics was introduced from the top by Peter the Great, only 3 centuries ago. Therefore two blues exist. The colour names are chervenyi, zholtyi, zelyonyi, goluboi & sinii, and being the language modern, they are clearly more or less R, Y, G, SB & DB. If you want to include the purple region, you can take purpurovyi as P. There is a misconception that Red is krasnyi, but that was a political hoax from 1917, when a decree was issued to change the word. The idea was that then people would like better the colour Red. (Krasnyi originally meant "nice".) You can check this in history: the nicest square of Moscow was already Nice Square = Krasnaya Ploshchad' in the time of Ivan the Terrible in XVIth century. It was nice, being a regular square, and nicely paved. Of course, it was not Red at all. For the different systems, see App. D too.

Maxwellian additive mixing (lights) uses 3 fundamental lights. In algebraic sense they might be anything; but we cannot mix negative quantities. So if we do not use colours quite apart, the mixtures will not be saturated. So we use R, G & B.

With paints the mixing is physically subtractive. Then the best triad is magenta, yellow & cyan. Magenta is practically purple, so P, Yellow is Y and the paint Cyan is BG. This is again a strong reason to regard Aristotle's kyanon as BG.

And now again: Tekhelet in Num (=4Mos) 15:38 is translated as Blue by Karaites, Israelites & Protestants, but as Purple by Catholics & Greek Orthodoxes. (Samaritans do not translate into English.) If anybody sees now which colour tekhelet must have been, he (in PC Indo-EUROPEAN convention he/she) is ready. If not, the text continues.

If you think that some text had become erroneous in the past, I tell you that such things may have happened, but not about a colour name. With the excavations at Qumran now there are material evidences that even the text of the Pentateuch was not exactly fixed before 2nd c. AD. Qumran texts sometimes agree with MT, sometimes (with or without translation) with LXX, which is the Ur-Text for Greek Orthodoxes, and which strongly influences the Catholic text of OT, sometimes it is between the two, and sometimes simply differs from both. But even before Qumran everybody knew that the MT Hebrew text was fixed ca. 150 AD, while the LXX is from IIIrd c BC, so simply they could not exactly agree short of miracles. But nobody really doubts that there was tekhelet in the Hebrew original of the LXX as well. The question is rather: can tekhelet mean purple?


It is impossible to answer definitely the above question. Surely at the edition of the first 4 books of Moses on the South (Judah, Benjamin, Dan & Simeon) tekhelet must have meant a definitely colour and/or a paint. (The Northern dialect somewhat differed from the Southern one, see Appendix A; and now almost everybody accepts that the first 4 book was edited in Jerusalem, while Deuteronomy came from the North.) The problem is that Modern Hebrew, from Middle Ages, do not use this colour name; it seems that Hebrew colour terminology was modernised, analogously to the Western & Central European languages. So, while surely tekhelet is a certain "blue", the more definite hue is a matter of argumentation.

Without giving definite references here, a search on Internet results in many studies which state that tekhelet is a blue, but some authors believe it greenish blue (maybe turquoise is meant), others sea blue (the Latin glaucus), others suggest a deep blue, maybe Prussian blue or indigo, or even purplish blue.

Other authors approach the problem from the paint. A pattern emerges, according which true tekhelet was a dye from the purple snail, but this process was very expensive, so instead of tekhelet often the Ersatz indigo was used.

This is an attractive solution; however because of 2 problematic points still we are not ready even if we accept this solution. Namely

1) there were two different "purple snails", from different genera, from Murex & Purpura; and

2) during the dyeing process the colour changes, and via trade tricks the final colour can vary between greenish blue and reddish purple (although surely the Phoenicians of Tyre developed the technique for getting purples, from bluish purple to reddish one).

In these years the organisation P'til Techelet claims to have solved the problem showing at Murex trunculus as the source of the paint tekhelet. However, even if Murex is the source, the answer is still not complete and this is the point where colour theory must step in (except if somebody claims e.g. Divine Inspiration, not unheard of in theology). Namely the juice from Murex trunculus can yield various hues (and do not forget the other snail genus of Phoenician purples, Purpura).

Namely, ancients knew it very well that the final colour of the textile depened on meteorologic & seasonal circumstances influencing solar light and on the exact way of the drying process. The original colour of the solution is pale, then it goes green, later "blue"; and the stained then dried textile can be anything from "blue" to reddish purple.

The reason is simple enough. Since 1909 we know that the agent dyeing Tyrian purple is 6,6'-dibromoindigo [17]. Now, let us go step by step.

Indigo is an efficient "blue" dye; for me it is deep blue on the verge of violet. Now, indigo's precursors are not blue but colourless, and they are converted to indigo via enzymes & oxydation (by natural air) [18].

Now, as told above, the agent in Murex is not exactly indigo, but even then nobody can be surprised that also the details of the drying influence the final colour, e.g. as "blue" on sunny days but purple on cloudy ones [18]. (Ancients, of course, dried the stained wool on stones in natural sunlight.)

The reason is simple enough chemically. Indigo has a strong shortwave reflection, but 6,6'-dibromoindigo, produced by Murex, has its absorption peak in 520 mμ, just in the middle of green. So it reflects short- and longwaves; and this is purple in the sense of the cerebral "inverse Gaussian" fits according to eqs. (5-7). Indeed, Godlove [9] found lots of purples, lilacs, fuchsias &c. when absorbing greens, while sky blue when the absorption was at 590 mμ, as for 6,6'-dibromoindigo in solution.

So far so good. But tekhelet cannot be just purple, because it is told that Tyrian purple is called argaman in the Bible. Now, Schatz [19] tells that 5,5'-dibromoindigo has indeed almost the same colour as indigo. Then there are at least 2 indigo-blue agents have been suggested for the tekhelet dye: indigo(tin) and 5,5'-dibromoindigo.

The differences of the 3 agents are subtle enough. Indigo has 2+2 rings connected via a double bond; and the 2 extremal rings are benzol-like. Now, in 6,6'-dibromoindigo 2 H atoms on the external rings in 6 & 6' positions are substituted by Br atoms; and in 5,5'-dibromoindigo the Br positions are different. Oxidation, UV &c. so can result in different shades, and so sowing at Murex (or Purpura?) is not the complete answer: it indeed must be appended by colour theory.

And using Aristotle, Maxwell and Weinberg the question gets an answer.

We saw that Ancient Greek colour system was "half a degree shifted" compared to Modern European. Now surely the translators of Septuagint, when writing Greek, used a system near to that of Aristotle. And Septuagint mentions phoinikun; using Aristotle's 5-colour circle, phoinikun is some hue roughly in the interval between deep blue & scarlet. Colours just outside this interval would have called kyanon on one side and halyrgon on the other.

On the other hand, when modern translators want to name tekhelet with a simple word, they mention blue.

Then the permitted region can contain deep blues (as e.g. indigo), with maybe violets. It cannot include purple, because that would have been called argaman; but cannot include either sky blues &c. because they would have been translated in Septuagint kyanon, not phoinikun.

For a Karaite [1] this may, indeed, be enough: not any blue, but roughly a range on the colour circle of Fig. 2 defined in the following way. The "left" end is somewhere between SB and DB, and the right end is cca. halfway between V and P. More "greenish" shades would appear in LXX as kyanon, while more reddish ones would appear in MT & SP as argaman.


Useful discussions with R. Svoboda about the Bohemian colour names & the louse theory of Slavic linguistics are acknowledged.


The prophet Jeremiah was born in Anatot (Benjamin), from priestly family, near to Jerusalem. However, Komoróczy [20] suggests that the family originally lived on the North, and got to Anatot when King Salamon exiled Priest Abiathar thither (1Kings 2,26). The argument is partly linguistic.

In the pronunciation of Jeremiah's name the Protestant and Hebrew traditions differ, although both use the Masoretic text. The alternative is Yiremyahu/Yirmeyahu. Of course, the Jamnia Canon was consonantal, but later the Masoretes reconstructed Yirmeyahu, i.e. Yirme-Yahu, cca. Yahwe uplift me (the root rwm).

However the Septuagint, in vocalised text, gives Ieremias. Here of course, the final -s is the suffix of the Greek MascNom, so this suggest cca. Yirem-Yahu. Of course, Protestant Churches inherited this reading from Septuagint, which otherwise they refuted.

Komoróczy gives an explanation for the Septuagint reading. First, we know the Syrian prince Yarim-Lim of Alalah, just North of the Orontesfrom 18th c. BCE. His palace is quite well known. Being the language also Western Semitic, the same root can be present in this name. Second, there was a root rym in Old Hebrew, meaning cca. "give". Later the rym was not used anymore and in a late period (for any case, after the Septuagint) Yirem-Yahu was interpreted via folk etymology as Yirme-Yahu.

Now, W. von Soden [21] mentions that the same "forgotten" root can be found in the name Miryam, which was always thought to be mysterious. Briefly, the use of the name Yirem-Yahu was Northern tradition in the Southern Kingdom.

Experts claim that the prophetic speeches of Jeremiah are more similar to the Northern prophets (e.g. Hosea) than to the Southern ones [22]. We may indeed accept that the family of Jeremiah kept Northern traditions, out of place in the South. Yarim-Lim was even more Northern than Hosea & Priest Abiathar.

As for the Samaritan Bible its dialect clearly differs from that of MT, and it is well-known that a significant part of the famous “6000 differences” are coming from the differences of the 2 norms. An analogy for this phenomenon is English/American. English “-our” is automatically transcribed into “-or” in USA, still Beowulf’s original is neither Queen’s English nor Harvard English. Either the Bible remembers correctly and Samaritans, having descended from Mesopotamian colonists, learned Hebrew, or, as they remember, they are the remainders of the Joseph tribes refusing the connections with David’s Jerusalem, the situation preferred the formation of a distinct dialect anyway.


When Galileo started to defend the Copernican cosmology, still in the court of the friendly Medici duke, Lorini, a Dominican brother in Florence, made a big sermon against Ipernicus, the heretic. Galileo wrote an angry letter telling that Copernicus was right, Lorini does not even know his name correctly, so is an ignoramus, and anyway, he should not mix into astronomy. Lorini's answer was indignant. He told that really, cosmology is not his true business, but he is sure that this Ipernicus or whoever was a heretic, and by the sermon he wanted only to demonstrate that he exists and has his own opinion. This Appendix, similarly, is not too important about blue, but why not to show that I know what I speak about?

The readers can see there that I am not a bigot devotee of consecutio temporum. Yes, I am a physicist, so I am keeping the meaning unequivocal. Language is a very important tool, but only a tool.

After many centuries of mutual accusations, the descendants of the original people taking Pentateuch seriously must gradually begin recognising that the differences between the texts in the Holy Writs of different religions are not the results of sacrilegous falsifications but natural consequences of the way the text was preserved during 1st millenium BCE. We can believe in the correctness of a copying after the elaboration of the Masoretic checking procedures, so MT indeed is a correct copy of its original; but we do not know how old was its original. We have texts of MT roughly 1000 years old; but also, from history and from the existence of variants in Qumran we can see that this text must have been fixed in Jamnia, in 2nd c. CE. This text may have been earlier one of the alternative variants, or it might be a product of construction/reconstruction using more than one texts.

Now we (almost) have 3 independent editions of the earlier text of Pentateuch. One is of course MT, used by the religions Jewish, Karaite & Protestant, the first two in the original Biblic Hebrew language. The second is Septuagint, referred here as LXX. (The "almost" will be explained immediately.) LXX goes back to an otherwise unknown Hebrew text of Pentateuch in 3rd c. BCE, translated to Koine Greek, surely in Alexandria. The original of LXX obviously differed from MT, and according to the Qumran finds in 1st c. CE the differences were within standard deviation of the various texts. LXX is the Ur-text for Greek Orthodox Church, and it is the most important source for the Catholic Church.

The third edition is the Samaritan Pentateuch (Sam), in Hebrew, but not in the same dialect as MT, edited by the independent Samaritan Church. Surely the text has its independent life at least since 2nd c. BCE; we do not know anything certain about the principles of copying afterwards.

While other texts also exist in Syriac, Armenian &c. translations, here we may stop, not to confuse Colour Theory and Philology.

It is technically difficult to compare the 3 texts, although proper polyglot editions exist since 16th c. CE, because the 3 texts use 3 dialects of 2 languages with 3 different alphabets. In addition, LXX's original Greek text vanished with the Alexandria Library. However we do have texts from IIIth c. CE, and the complete Bible in Codex Sinaiticus from IVth c. CE, so the original LXX is fairly reconstructed. For further references see [23] and citations therein.

No reliable English translation of SP is available yet to compare it directly with, say, KJV. However even now the triple comparison is possible for the immediately following Book of Joshua. (It is not the part of the Holy Canon of Samaritans, but still a recognised text.) Greenspoon is translating this part of LXX and some preliminary texts have been published in [23]. Let us see e.g. Joshua 5, the camping in Gilgal.

(The English translations of) MT and LXX slightly differ. However in both Verse 1 is the impact of the news about Joshua crossing the Jordan on the Syrians, Verses 2-9 is a story about Joshua circumcising the warriors who were not yet so, and 10-12 speaks about the cessation of the manna flux.

MT and LXX tell exactly the same story, but not always with the same wording. E.g. in Verse 2 MT tells that this was the second circumcision; LXX does not tell this. In the next Verse LXX tells that Joshua "made sharp flint knives", while MT tells simply "made flint knives". In Verse 12 LXX mentions the "country of the Phoenicians", while MT the "land of Canaan". And so on.

Now, the Book of Joshua is not holy for Samaritans (although there is a theory that earlier there existed a Samaritan Hexateuch [24]), but the Joshua tradition is honoured by them. So the Samaritan edition of Joshua is the main part of the Samaritan Chronicle, known in Arabic. (Different Chronicles exist, cca. as 1 & 2Macc.) An English translation is available as [25]. There Joshua 5 is the last third of Chap. XVI and the beginning of Chap. XVII, but only Verses 1 & 10-12 of the above versions; the circumcision story is absent.

As for the Septuagint, it is told that SP differs cca. in 6000 details from MT, but in this 6000 it goes together with LXX at 1900 places. Qumran expert Vermes shows 2 interesting examples [26]. The first is Exodus(=2Mos) 10,5, where MT and LXX are identical (except for the fact that LXX is Greek). There SP is longer, and it seems to completely agree with the 4Q Qumran text (at least in the characters contained by the fragment). However in the second case, Deut(=5Mos) 32,43 4Q is halfways between LXX and MT (while in 2Samuel 8,7, which is, of course, not preserved in Sam, 4Q is almost identical with LXX, and both are much longer than MT). E. Deutsch (in a posthumous book [27]) explicitly mentions some differences between SP and MT. E.g. in Exodus 13,7 SP and LXX agree against MT (although I must confess, I do not see the difference, but I am a physicist), and there is a theologically very interesting point in Exodus 27,4. Here Moses orders that the people shall erect stones with the Dekalogus, painted white with lime (and also an altar). Now MT tells that the proper place is Mt. Ebal, while SP tells Mt. Gerizim. (They are neighbors.) Now the present Catholic text mentions Ebal, but (it is told; I did not check) the Vetus Latina mentioned Gerizim, so LXX might have mentioned the Gerizim of Samaritans.

I think there I stop. Namely, I have no doubt that in Num 15:38 all the three Hebrew texts wrothe "tekhelet" for the colour of the string. At least E. Deutsch concludes that for definite ordinances of Moses SP differs from MT only in 2 points, at Ex 13:7 and at Deut 23:18. Num 15:38 was never disputed, but the meaning was and is.


While people can argue to and fro which is the par excellence Red (while the other hues are mixed with Yellow or Blue), physically & biologically the Ideal Red is well defined. Namely, consider the 3 cone receptors in the majority of human eyes. (For a part of daltonians the problem does not exist at all, while for tetrachromats our argumentation would still remain valid, mutatis mutandis.) At extremely long wavelengths only the sensitivity of one type of the cones survive, that of the Red cones. So if we compensate the decreasing sensitivity with increasing intensity the limiting colour is the Reddest Red.

While this construction seems valid without discussion, the validity is not so trivial. The statement is conform with colorimetry, but is rather strange in evolutionary context. The existence of mammalian trichromacy is rather new; higher Primates are trichromats for no more than 20 My. The Red and Green cones forked from their common ancestors, the Yellows, so one would expect common limiting sensitivities.

That is indeed true, but only for non-visible infrared above cca. 1000 mμ. The seeming contradictio in adiectis is dissolved if we remind that there is no sharp border of vision. Under experimental circumstances such longwave lights of huge intensities can be seen, and the impression fluctuates with changing wavelength from red to orange or even yellow, and back [28]. There the common ancestry shows indeed up.

Now, with decreasing wavelength the Green cones also start, and the colour of a monochromatic light starts "to contain some Yellow". This is Flame Red. In the other direction lies first Cherry Red, then the already slightly bluish hues. It is not clear if Cherry Red can be produced with monochromatic light (so that is it the Ideal Red, or not); the two principal problems being the subjectivity of the border between colloquial Red hues, and the ambiguity in the word "cherry" in English (for which I will briefly return in Appendix D).

Obviously the above construction is impossible for middle wavelengths. There is no physical light exciting only the Green cones. (By using the trick to wear out transiently the Red and Blue cones with intensive purple light and then switching to a green monochromatic light some observers were able to get impressions "greener than the greenest green", but this trick has no physical meaning.

Now, for short waves the Red construction should be possible, but it seems not so. For extreme short waves most observers report Violet, a hue which "gets back" some Red. This fact (?; see immediately) is reflected in the colour coordination of the Commission Internationale d'Eclairage (CIE/ICI), where the extreme "Blue" end of the spectral loop (i.e. the locations of monochromatic lights) somewhat turns back. (You can see this canonical loops anywhere; for a formal reference see e.g. [13].) The simplest explanation of this phenomenon would be a secondary small peak on the sensitivity of the Red cones about cca. 445 mμ.

The problem is that biology does not observe this secondary peak. Also, a minority of people stick to the idea that "Violet does not exist". I met this viewpoint most explicitly while discussing colours with a couple: physicist wife & engineer husband. The wife (who, interestingly enough, seems to be a tetrachromat) reported her "Blue" impressions exactly as myself, but the husband was adamant that there is nothing new at the shortwave end of an artificial rainbow produced via prism; and told that we simply "make up the thing" by verbal tricks.

The first person demonstrating that some fundamental must lie behind this "curving back" was Weinberg [11]. He showed that Parametrisation (5)-(8) (in the brain) is good for colour constancy and in the same time results in Gaussians there; and such assumptions of the brain would be quite good for physical illuminations and reflectances. (I know the argument cannot be understood; if you are really interested, read [11].) Now, from a Gaussian basis one would get a spectral loop of the form of a conic curve; and the CIE loop is indeed quite hyperbolic; except for the very shortwave end. Observe that not the general "curving back" is to be explained: that starts already at 500 mμ, greenish blues, but there the shape is excellently hyperbolic. The true problem is the deviation from the hyperbole from cca. 475 mμ. The situation can be visualised on Fig. 3, where the approximate loci of the 11 cornerpoints of Fig. 2 are also indicated.

Fig. 3: The 1931 CIE colour triangle, with the approximate loci of the 11 “most important colours” of Fig. 2.

I have made a simple but analytic realisation of the Weinberg model in [12]. There, as Weinberg suggested, bright purples are inverse Gaussians with a depression in middle wavelengths. Now, Weinberg's "Gaussian basis" blows up for too saturated purples (in a more physical language some "purple catastrophe" occurs, resulting in infinities. It is just possible that the violet deviation (from hyperboliticity) is somehow the result of a compromise to have a basic as Gaussian as possible without divergences. Again, I know I cannot be understood; but you can read [12].

Anyways, because of the strange shortwave behaviour of human eye/brain there are problems with the Terminal Blue; it either does not exist or it is the Extreme Violet, but Violet does not seem the Ideal Blue. In addition our colour distinction is very good at short waves, so we do see the differences (but somewhat ignore them in Western & Central Europe).

For the longwave end, where the limiting monochromatic waves do realise something Ideal, I chose the language that Ideal Red is Carmine, Vermillion is a shorter wavelength, but still in the red sector, while Scarlet is near to the red end, but already on the purple line, so it can be realised only by the mixture of a longwave and a shortwave monochromatic light. My language may or may not be accepted; it is possible to ask people of English/American/Scottish/Australian/&c background about colour names for monochromatic and mixed lights; only I do not want to postpone this study until that; and I would expect an equivocal result anyways.


Words for Reds are not so trivial as we (at least males) mostly believe, including [15]. We may believe that there is one generic word for Red, but this is generally not true. Maybe it is true for English, where "Cherry Red" means something obviously longwave (when heated up, the iron oven is first Cherry Red, so this has the lowest colour temperature). Then the arguments of [15] apply: Red is the generic term, and Cherry Red is within the Red class. For any case, observe that English Cherry denotes two fruits. One is the Slavic "cheresnya", Magyar "cseresznye", clearly the same root as in English, but this fruit is not Cherry Red for colour, but Flame Red (or at least Vermillion). The other fruit (the Sour Cherry) is Cherry Red, but its Slavic name is "vishnya" (the Magyar is "meggy"), so linguistically this is not the par excellence Cherry.

In unequivocal botanic terms the flame red/vermillion cherry is Prunus avium, diploid, so the situation is simple (and the Japanese cherries...?), while the cherry red sour cherry, Prunus cerasus is allotetraploid, so maybe it was hybridised in Neolithe. Then the par excellence cherry is not cherry-coloured. As I told, I am not sure if the colour of the sour cherry, the Cherry Red, is Extreme Physical Red, or it contains already a small amount of Blue.

In 1990 I visited Erlangen and there (quite apart from the aim of the visit) discussed colour systems with an Egyptian Arab colleaague, M. A. Abdel-Raouf. We showed coloured objects to each other and named them in English, (Egyptian) Arabic & Magyar. Then we lost contact, so for my knowledge the only output so far is a Figure in [29]. Anyways, an approximate Colour Triangle was constructed, which is easily translated into a colour circle. I do not guarantee the canonical transliteration, although I made my original notes still in the presence of M. A. Abdel-Raouf, but surely the names will remain recognisable. For convenience I start from Middle Purple, a well defined point, and go Redward.

Middle Purple is Banafsigi. Then come Tobi, which is either Cherry Red or Scarlet. Then Ahmar, which is definitely Flame Red. The next is Burtikali, more or less Orange. Azfar is approximately Yellow. Zarei is not yet our purest Green, but rather Leek-Green, or Aristotle's Prasinon, or maybe something between that and Green; for any case a Yellowish Green. The next is Ahdar, already somewhat beyond Green, with a "coldish tinge", so a Bluish Green. The next is Fozdoki, and we are not yet at Turquoise. That is the next, with the name Turquise. Then comes a (not Deep) Blue, Bambi, which was reported to be sky-colour, so more or less the Latin Caerulus, the Russian Goluboi. Next is the more or less Violet (or Indigo?) Azrak, and then we reach again the Middle Purple Banafsigi, closing the circle. Fig. 4 is a schematic picture.

Fig. 4: Attempt to visualise the Egyptian Arab colour system.

Errors are possible here and there, but observe that Arabic uses more simple colour names than claimed universally in Ref. [15]. Namely, the names are not professional terms of textile engineers & women (as English Vassar Rose, Beige, Mauve & such), but used by males. All the 11 colour names use single words of different roots. So much about Generic Reds, the universality of colour schemes [15] and such constructions of scholarly mind.

Of course almost anything can be forced into prearranged schemes. E.g. you can discover the 4+1 colour system of Central European Slavic languages, which I give here in a Generic Slavic (meaning that something Average Slavic), without diacritics, transliterated Englishwise. For later discussion I give the Magyar too, and of course the English equivalents, as follows. Moreover I append the Table with 3 other colour names, to reach the level of [15], which claims the universality of the basic colour names. I will not distinguish Purple and Lilac; for me Lilac is a Purple.




The 4 Pure Colours













The exceptional colour of Heraldry




Another Bright Hue




Fundamental Pastels







Table 8: A comparison of important Slavic, Magyar & English colour names.

Do not ask me, which Slavic is here; for a Magyar speaker all Slavic people are at the verge of mutual understanding. According to Hungarian tradition, Generic Slavic is Slovakian [30], and linguistically it is somewhere at the middle of Slavic languages (at least, according to Slovakians), so I based the Slavic on Slovakian if ambiguities occurred.

The idea of [15] is that the 11 basic names (these + white, black & gray) appear in any language in a predetermined sequence. In Phase 1 white & black, but they are not colours. In Phase 2 Red. In Phases 3 & 4 Green & Yellow. In Phase 5 Blue. In Phase 6 Brown, and in Phase 7 the remaining ones. Not all languages evolved to the present level of (of course) English (circumscriptions, compound words, clearly fresh borrowings &c. are of course not taken into consideration.)

Then English is past Phase 7, Slavic is in Phase 7 (oranzhovy and purpurovy are recognisable loanwords and ruzhovy is a simile from "rose"), and Magyar is hardly better. However...

Do not forget that Slavic is Indo-European. If you read English, you should recognise the Slavic roots as well (and if you do not read English, there is no problem at all).

Now, can you recognise them from English (or, maybe more naturally, from German)? Red is Rot in German, but Cherveny is something unique. I hesitate if I could recognise Yellow=Gelb in Zholty, but I bet that Zeleny is quite strange for you for Green=Grün. (It is not so strange for me; we shall see, why.) As for Blue=Blau, Modry is foreign even for Slavic Russians (who have 2 separate Blues). For Brown Hmedy is not too related.

I should go through Magyar, demonstrating that an Indo-European cannot recognise Uralic roots. You, however, will be surprised. Red is Piros, and Greek Pyr is Fire. With a high probability, that Basic Colour Name in Magyar comes from Greek. Green, Zöld, definitely comes from Indo-European Iranian (most probable, Alan). And, although you may not see it, Blue & Yellow, Kék & Sárga, come from Turkic, very probably not from Common Turkic but Bulgarian: Kök & Sarig. (The Old Turkish Chief Deity, the Blue Sky, also the Lord of Genghis Khan, was Kök Tängri; now in Magyar Kék Tenger is Blue Sea. Also big enough.) You also cannot see, but Purple, Bíbor, is Purpur/Porphyr, either Latin or Greek. Barna is clearly the same as German Braun, which is just the English word, but with a more complicated orthography. Narancs is the same fruit as Orange, only we took the word via Italian (where the fruit goes back to Roman times), not French. And finally to embarrass the readers, I note that Gray, which is, true, not colour, but according to [15] belongs to the most evolved Phase 7, Szürke, seems to have come into Magyar from Chechen (I am serious: Siri). Since Pink, Rózsaszín, is a simile (a rózsa színe=the colour of the rose), is the Magyar here without any genuine colour name of its own?

OK, then let us go more deeply. Whither have gone the root of Red=Rot from Slavic, and why Cherveny there instead?

The root is there in Bohemian (or as President Klaus forced it onto some Englishpeople, Czech). It is Rudy. Clearly Rudy~Rot=Red. It is a red colour of flags, "only" not that of the Hungarian or Bohemian flags, but that of the Soviet. (Therefore the leading Bohemian newspaper was Rudé Právo = Red Truth. It was not Chervené; Rudy is the proper colour of the Revolution of the Proletariat. Because Rudy is The Colour of Blood.)

Cherveny means Worm Colour. Cherv is Worm (of indefinite type). There is a Bohemian linguistic theory for the reason: there was a worm, used on the Balkan Peninsula & Asia Minor, whose juice was used to colour textiles brilliant Red. (Not Purple; it is Vermillion.) The "worm" is a louse (a coccideal), Kermes vermillio, living on oaks. Almost the same thing as the purple marine snails Murex and Purpurea, of course, different phyla, but all Protostomata. (In Magyar, the word appears as "cser", and means something from oak trees, not for colouring, but for developing leathers.) The root rudy is not present in Slovakian, but maybe existed in older times.

So 2 Reds exist Bohemian. Now, there is 2 too in Magyar. In Table 8 I gave Piros, Flame Red or Vermillion from the Greek Pyr, Fire. However there is another, Vörös/Veres. Blood is Vér, so this is clearly Vérszínű, Colour of Blood. (And this is the only colour name common between Magyar & Manyshi, our nearest linguistic kin in Western Siberia. The other colour names are not!)

Now, is there a Generic Red in Magyar or not? It is a matter of opinion. There are, for example, Fundamental Laws, which can be modified only by explicite 2/3 majority (2/3 of all MP's). National symbols, so the flag and the heraldry are such. Now, the Red-White-Green flag is Piros-Fehér-Zöld; the Soviet flag was Vörös, and the Red Cross is Vöröskereszt. The Red, White and Green dominate also in the escutheon of the nation; but there the Red is Vörös. It is never confused. It is possible to state that blood is "piros"; it is also possible to state that the fire is "vörös"; still if you ask people, they tell that piros may contain a small amount of yellow, while vörös does not have yellow component, but it may contain a small amount of blue.

So: Vermillion & Scarlet. Flame Red & Cherry Red. Ahmar & Tobi. Cherveny & Rudy. Piros & Vörös. So much about Generic Reds, prearranged Phases of Linguistic Evolution & such. And: how long live colour names? Slavic Cherveny is Common Slavic, so maybe 1500 year old. Magyar took the names of 4 Pure Colours in Table 8 during the Migrations, bw. 6th & 8th centuries CE. And the Western Europeans?

The 4 English Pure Colours go back at least to Common Germanic, maybe more. But French "bleu"=Blue is obviously neither Romance nor Celtic, but German, surely from the Franks.

Italian is even more demonstrative. Let us see the 6 heraldic tinctures (gold is yellow and silver is white). I make again a Table, now for Italian, Latin & English. Namely historically Italian is the Romance language least influenced by superstrates, and without substrates from Roman times. So the most Latin roots should be preserved, and generally it is so. But for tinctures...


Italian Colour




Albus, Candidus



Flammeus, Luteus, Ruber, Rufus



Croceus, Flavus, Fulvus, Helvus



Prasinus, Viridis


Blu, Azzurro

Cerulus, Lividus



Ater, Niger

Table 9: Medieval Heraldic tinctures in English, Italian & Latin.

The Italian system is clearly not the Latin one (and has two Blues). But the roots are also not the Latin ones!

More definitely: for white neither of the 2 Latin roots survived. Recent Bianco is German; only it is rather Black there. ("Without colour".) Rosso comes from a colour name in Latin, but not for Red, but it was pastel Roseus, a simile even for that. All 4 Yellows of Latin went out of use, Giallo is new, maybe the same as French Jaune, and maybe German. Viridis survived as Verde, but the 2 Latin Blues are lost, Blu is obviously German, and I do not know whence is Azzurro. For Black Latin Niger has survived.

A completely new system and only 2 roots for the 6 places; a poor survival for 1600 years without serious superstrate and no substrate at all! But of course, the system of heraldic tinctures were imported, and it was simple then to import the technical terms as well.

So much about connections of recent colour names with the origin of nations and languages. Now, on the examples of Italian & Magyar it is not at all surprising if Hebrew left out 3000 year old tekhelet, and now seems to use new words & new colour scheme.

Early Medieval Europe was not too interested in purple paints except for Byzance; there the Emperor imported the textile from Phoenicia. European warriors & merchants were not so rich, but they liked bright red clothes, so paid for it to Balkan manufacturers, who extracted the paint from a louse, so the Slavic consumers called the colour "wormy", "cherveny", and now it is the Basic Colour Name of them for Red.

Central Europe even had a purple paint from a worm, Margarodes polonicus. But it produced a reddish purple, not a bluish one.


For finding the proper names for Red+ (the yellowish/warm neighbour), Red0 and Red- (the bluish/cold one), we can turn to the painting softwares, or to Wikipedia. I used the latter one, and some interesting names I organise into a Table as:





Colour of:






Cardinals' clothes; vivid Red












Purplish Red







B, D











Beyond 630 mμ; Oxigenated blood






Redder than vermilion












Bw. 380 & 420 mμ


Table 10: “Red & purple” colour names vs. RGB coordinates according to Wikipedia.

This would suggest the sequence Vermilion -> Scarlet -> Crimson, but...

Let us see now the Notes:

A) The Magyar word for a Cardinal is Bíboros; Bíbor=Purple, and they are the Princes of the Church, that is the reason of wearing Purple. Indeed the RGB coordinates indicate some Purple, not a vivid Red. Now if clergy is called scarlet (as the Babylonian harlot), why to compare it to yellowish red, not bluish red?

B) So blood and blood differ for colour; so arterial one is without Blue, venal does contain it. But there is no artery either in the mouth or at the nails. So if a femme fatale (a scarlet woman) applies Blood-coloured rouge & nail polish, they must have blue contribution.

C) This Cerise is purplish. But it is not the colour of Slavic "cheresnya", Magyar "cseresznye", Cherry, but that of Prunus cerisum, the sour cherry. So Cherry Red is indeed beyond Red.

D) Now you cold tell that I simply should use Crimson instead of Scarlet. But I have my doubts. Namely Crimson comes from Kermes, the worm genus producing bright Red paint, more exactly the species Kermes vermillio. So the colour Crimson should be the same as Vermilion. Now look at the Table: Vermilion is towards Yellow, Crimson is towards Blue. The conclusion that the names are confused is hard not to be drawn.


[1] Karaite Korner: Tzitzit.

[2] Bekker I. (ed.): Aristotelis opera. Academia Regia Borussica, Berolini, 1831

[3] Barnes J.: The Complete Works of Aristotle. Princeton University Press, Princeton, 1994

[4] Newton I.: Opticks: or a Treatise of Reflections, Refractions, Inflextions and Colours of Light. Innys, London, 1730

[5] Young T.: On the theory of light and colours. Phil. Trans. 92, 20 (1802)

[6] Maxwell J. C.: Theory of the perception of colours. Trans. Roy. Scottish Soc. of Arts. 4, 394 (1856)

[7] Lukács B.: Did Green Stars Exist 4000 Years Ago? In: A. Rácz (ed.): Proc. ERŐFI II, KFKI-1995-11, p. 187

[8] Gerrold D. & Niven L.: The Flying Sorcerers. Benbella, Dallas, 2004

[9] Godlove I. H.: The Limiting Colors Due to Ideal Absorption and Transmission Bands. J. Opt. Soc. Amer. 37, 778 (1947)

[10] Eisenhart L. P.: Riemannian Geometry. Princeton University Press, Princeton, 1950

[11] Weinberg J.: Gen. Rel. Grav. 7, 135 (1976)

[12] Lukács B.: Acta Phys. Pol. B19, 289 (1988)

[13] MacAdam D. L.: Specification of Small Chromaticity Differences. J. Opt. Soc. Amer. 33, 18 (1943)

[14] Lévi-Strauss C.: Tristes tropiques. Libraire Plon, Paris, 1955

[15] Berlin B. & Kay P.: Basic Color Terms. Their Universality and Evolution. University of California Press, Berkeley, 1969

[16] Gyökösy A.: Latin-magyar szótár. Akadémiai Kiadó, Budapest, 1963

[17] Friedländer P.: Über den Farbstoff des antiken Purpurs aus Murex brandaris. Ber. Deutsch. Chem. Ges. 42, 765 (1909)

[18] Huxtable R. J.: The Mutability of Blue. Mol. Intervent. 1, 141 (2001)

[19] Schatz P. F.: Indigo and Tyrian Purple -In Nature and in the Lab. J. Chem. Edu. 78, 1442 (2001)

[20] Komoróczy G.: Bezárkózás a nemzeti hagyományba. Századvég, Budapest, 1992

[21] Von Soden W.: Mirjam-Maria: "(Gottes-)Geschenk". Ugarit-Forsch. 2, 272 (1970)

[22] Wilson R. R.: Prophecy and Society in Ancient Israel. Fortress Press, Philadelphia, 1980

[23] Greenspoon L.: The Book of Joshua, Part I. Curr. Bibl. Res. 3.2, 229 (2005)

[24] Hjelm Ingrid: What Do Samaritans and Jews Have in Common? Recent Trends in Samaritan Studies. Curr. Bibl. Res. 3.1, 9 (2004)

[25] Crane O. T. (ed.): The Samaritan Chronicle. J. B. Alden, New York, 1890

[26] Vermes G.: A holt-tengeri tekercsek: Negyven év után. MTA Judaisztikai Kutatócsop. Értesítô, 1992 N° 6

[27] Deutsch E.: Literary Remains of the Late Emanuel Deutsch With a Brief Memoir. H. Holt & C°, New York, 1874

[28] Griffin D. R, Hubbard Ruth & Wald G.: J. Opt. Soc. Amer. 37, 546 (1947)

[29] Ágnes Holba & B. Lukács: The Triality of Our Colour Vision. In B. Lukács & al. (eds.): Trialities in Evolution, KFKI-1995-21, p. 60

[30] Marsina R.: Ethnogenesis of Slovaks. Human Affairs 7, 15 (1997)