Zenzizenzizenzic
en.wikipedia.org
en.wikipedia.org
Z(enzi)z\1z\1c
I hope I remember this word if I ever have to teach how LZW compression works. It's better than 'banana'.
Now that's what I'd call a classic definition.
> Table of powers, symbols and names or descriptions form 0 to 24 by Samuel Jeake, written in 1671 Therefore, a number raised to the power of six would be zenzicubic, a number raised to the power of seven would be the second sursolid, hence bissursolid (not a multiple of two and three), a number raised to the twelfth power would be the "zenzizenzicubic" and a number raised to the power of ten would be the square of the (first) sursolid. The fourteenth power was the square of the second sursolid, and the twenty-second was the square of the third sursolid.
A truly awful system.
Almost no one will attempt to parse SMILES for non-trivial molecules by hand, but almost every computational package can easily parse them.
Nobody in it's right mind will ever call it by it's real name except maybe to sound more intelligent. Most important molecule have short names either based on the standard or given names.
Eg 2^12 being written 2^(223) has clear advantages
Well, for certain values of "real" :)
You know why complex jokes are not funny? Because the joke part is imaginary.
(I'll see myself out.)
1 + c_1 a^2 + c_2 a^3 + ...
One wonders which came first. It may be that the notation followed this focus on individual terms, but it is interesting that no one considers "expanding" transition amplitudes in infinite products or continued fractions. Also, there certainly exists much more knowledge (theorems, technology) around series than products AFAIK. Again, I don't know which came first because I don't know too much about math history, but it seems reasonable that the causation may be reversed.
There are very good reasons for this. The whole observation is basically the same phenomenon as someone observing, "you know, 34,825,119,276 and 35,174,884,395 are basically the same number for my purposes; I'll just call it 3e10 or, if I'm being really fancy, 3.5e10".
In these applications, the series variable is a very small number. The higher exponents given to it in later terms of a taylor series cause those terms to be very small compared to the early terms. That's why we take the early terms as an approximation to the whole thing -- we have chosen our representation so that that will be true.
(This is the entire reason for Taylor series in the first place -- a Taylor series is a Maclaurin series adjusted so that the variable can be small for purposes of the series, no matter what its absolute value might be.)
Series notation is just "this is a like a polynomial, but it goes on forever, so here are the first few terms."
It's a bit more ad hoc, because pre-pending a name multiplies the exponent (rather than adding, as Roman numerals do) -- making primes impossible to express. So they need the notion of a "sursolid" to express exponents (like 5 or 7) that do not factor into twos and threes.
So, amazingly, he was able to create a system more ad hoc than Roman numerals.
Or Calculus in Newton's book. The techniques were sound, but you'd have to be a superman to work the way he did.
Mathematical notation allows for better "chunking" and reduces cognitive load.
The thing is, he worked really hard to avoid calculus because it was too new and not widely accepted. Whenever he could give an argument without calculus, he would. It is hard to read but because he's trying to write calculus in the style of Euclid. So most proofs that would involve limits or derivatives would be written in a really roundabout way in terms more familiar to people at the time used to Euclid's geometry. This style of argument survives today in relics such as the geometric proof that lim sin(x)/x = 1 as x -> 0:
http://math.stackexchange.com/a/75151
Not only supermen were able to read the Principia, as obviously it was read and its ideas spread far and wide, but perhaps modern supermen would be required in order to see the actual calculus behind the veil of Euclid that Newton had to cast it at the time.
I actually do read an English translation of the Principia from time to time for bedtime reading, and it's not that impenetrable.
And of course the actual calculation of this function had to be done (up to a factor of 2) all the time during navigation until things like GPS appeared. See https://en.wikipedia.org/wiki/Haversine_formula
I remember this one from high school (1999/2000). Is "verseno" (Spanish).
When would you need to refer to versions by name?
I'm sort of wondering if that terminolgy sounded more natural then because in "older" English, closer to Germanic roots, it was natural to create new words by pasting together morphemes.
Well that explains it.
https://en.wikipedia.org/wiki/Names_of_large_numbers
Thankfully, just like numeric exponents make Zenzizenzizenzic obsolete, exponential notation mostly makes large number names obsolete.
Vierzig for example means Forty (Vier = four, plus the suffix). Interestingly it's not as simple for other numbers where the base of the word gets butchered a bit like in english. So as it's "Forty", not "Fourty" it's also "Zwanzig" (20) not "Zweizig".
All that makes me wonder if it really ever meant 'squared' or was rather a old form to build number >100. If Neunzig is 90, Zenzig sounds like it could be 100.
A bigger problem is that it's one letter longer than the Scrabble board admits.
http://quod.lib.umich.edu/e/eebo/A95751.0001.001?rgn=main;vi...
For example, x^4 would have been thought of as a square of a square, with all the geometric meaning that that entails, moreso than as a convenient way to express x * x * x * x. People wouldn't have cared about x * x * x * x, but they might have been interested in the properties of squared squares, hence the oddball naming schemes.
People reasoning about problems involving x^4 would have likely been using verbal proofs involving geometric concepts than using the notation everyone uses today, and in that context x^4 is the square of a square rather than simply being an instance of x^y in which y = 4.
Grain of salt though- this isn't my field, somebody please correct me if I'm wrong!
https://en.wikipedia.org/wiki/Euclid%27s_Elements
They aren't really books of equations, just lots and lots of verbose axioms and theorems and conclusions about properties of points/lines/triangles/circles/etc.
A square (the squaring operation that is, not the shape) in this context still means x * x, but it would be described (and reasoned about) in terms of being the surface area of a shape or the length of a line, and logically used in comparison to the surface areas of other shapes or the lengths of other lines. A squared square would still mean x^4, but it would be presented in terms of some quantity (x^2) which was shown to be the square of some other quantity (x), which also happens to be the square root of yet another quantity (x^4) according to the logic of whatever property the proof was trying to establish.
An example of a geometric property of the squaring operation could be a simple statement along the lines of, if the side of one (geometric) square is shorter than the side of another square, then the area of the first square is guaranteed to be less than the area of the second square. Which all sounds painfully trivial, to the point of not even being worth talking about, but in the context of Euclid it would have been a meaningful relationship that could be exploited as part of some much more elaborate proof.
At no point would any of this be expressed in terms of modern mathematical notation, it would all be semiformal verbal descriptions of the relationships between 2D geometric primitives. In the world of philosophizing about 2D geometry, squares and square roots have a conceptual primacy that other exponents do not have (likewise for cubes and cube roots in 3D geometry).
What little I've read of this stuff comes across like the machine language of mathematical deduction, where everything is built up from a very long series of very simple statements that (given enough statements) can eventually produce very sophisticated results. The way math is taught now (at least to non-math majors) comes across more like a very high-level language where we're simply taught rules like x^y * x^z = x^(y + z), and we aren't required to understand it in terms of low-level geometric proofs.
Another way to interpret it could be, "okay, take this cube with a volume, take that volume and pretend it's actually the width of another special mega-cube and never mix mega-cubes and regular cubes".
A square of a square is a square made up of squares :)
(like a Sudoku puzzle)