Saturday, December 28, 2013

Iubervox: a Latin Translation of Jabberwocky

Jabberwocky is the sort of poem that you can't help but love. It is a euphonic admixture of sense and nonsense, meaning and absurdity. One cannot help but get the impression that it is intelligible, and yet many of the words, especially the first stanza, are only real-sounding, and not true words (though since its writing, some have become bona fide English). The poem was a central element in Lewis Carroll's amazing work Through the Looking-Glass. Due to its uniqueness and playful nature, as well as its unorthodox vocabulary, it has been translated into many languages, including several renditions in Latin. I had seen these and was disappointed in them for several reasons:
  1. Most do not rhyme 
  2. Many follow ancient metrical conventions and not modern ones.
  3. Many stray too far from the original in terms of word sounds and meaning.
  4. Many do not even attempt to suggest etymologies for their neologisms, and many of these are not similar to the original words in sound, meaning and etymology (and some don't sound like Latin at all).
I therefore decided to write my own, in which I try to correct for these errors and even give proposed etymologies of my own. The following is the finished result.


A Luviso Carollo
Latinatum a Nadavo Cravito

Proligrium1, slemti2 torveri3              
In ubere4 gyrant5, egillant6:              
Plene minstei7 boregoveri8,            
Et momei9 rathmoi10 ecrepant11.                    

“Iubervocem12, mi fili, cave!            
Ungues capiunt, mordent fauces                    
Cave aves Iubiubes13, fuge                
fremiosos14 ducraptores15.”              

Tractat gladium vorpalem16:
longe manschomenum17 persequens –
Cessat prope Tumtum18 arborem
Diu ibi stat cogitans.

Ac dum stat hupice19 cogitans,
Iubervox oculis ignis cum
Per silvam tel’gam20 venit hifflans21,
Barbarillat22 venit dum.

Semel bis! semel bis! Per perque
Snix-snacem23 dat vorpal ferrum.
Abit mortuum, cum capite,
Calamferens24 venit rursum.

“Iubervocem cecederasne?
Radiacule25, i amplexum!
Dies frebiovus26! Calheu, c’lhae27!”
Cachinillat28 ob gaudium.

Proligrium, slemti torveri                  
In ubere gyrant, egillant:                  
Plene minstei boregoveri,                  
Et momei rathmoi ecrepant.


By Lewis Carroll

`Twas brillig, and the slithy toves        
Did gyre and gimble in the wabe:         
All mimsy were the borogoves,                       
And the mome raths outgrabe.            

"Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!"

He took his vorpal sword in hand:
Long time the manxome foe he sought --
So rested he by the Tumtum tree,
And stood awhile in thought.

And, as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!

One, two! One, two! And through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.

"And, has thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!'
He chortled in his joy.

`Twas brillig, and the slithy toves        
Did gyre and gimble in the wabe:         
All mimsy were the borogoves,
And the mome raths outgrabe.
1. Proligrium=Snack-time, [>Pro + ligurire]
2. Slemtus=Slimy and calm, [>exlemtus>ex + lim(os)us + lentus]
3. Torverus=Truffle/mushroom-eater, an animal, [>Tubervorus>Tuber + vorus]
4. Uber=Fertile field/soil
5. Gyrare=Spin, revolve, whirl
6. Egillare=Force out/dig/bore a little, [>exigillare, diminutive of exigere]
7. Minsteus=Flimsy and miserable, [>Mistenus>Miser +Tenuis]
8. Boregoverus=Northern gudgeon-eater, [>Boregobivorus>Boreus + Gobius +vorus]
9. Momeus=Ridiculing, critical, grumbling, [>Momus, Greek god of censure, derision]
10. Rathmos=A type of turtle, [>ραθυμος, easy tempered, lazy]
11. Ecrepare=Make chattering/rattling noise, [>ex+crepare]
12. Iubervox=Creature with a great voice, [probably>Iubere+Vox]
13. Iubiub=Large, aggressive species of bird , [imitative of call]
14. Fremiosus=Roaring, [>Fremere]
15. Ducraptor=Predator which seeks the leader of a group, [>Dux+Raptor]
16. Vorpal=Manly, destroying, keen, deadly, [Unknown origin, possibly related to vorax, verpus, orpax or Orpheus]
17. Manschomenus=Maniacal, enraged, mad, [>μηνσχομενος >μηνις+σχομενος (aor. mid. part. of εχω)]
18. Tumtum=species of fruit tree, [Reduplication of Tumor, for its large, swollen fruit]
19. Hypice=Out from under, secretly, [>ύπεκ]
20. Tel’gus=Telaugus=Far-shining, conspicuous, [>τηλαυγης]
21. Hifflare=Breathe heavily/noisily, [>Hiare+Flare]
22. Barbarillare=Speak gibberish, babble, [Diminutive or barbarire]
23. Snix-snax=Swishing, cutting, hitting sound, [Imitative]
24. Calamferre=Be victorious, bear symbols of victory, bear pikes/reeds [Calam+ferre>καλαμηϕορος]
25. Radiaculus=Shining slightly, smiling, happy [Diminutive noun form of Radiare]
26. Frebiovus=Worthy of praise, celebratory, to be honored/celebrated [>Fere+bis+Iovis, literally, nearly twice Jove]
27. Calheu/Calhae=Cries of joy/laughter [Unknown origin, possibly imitative or καλη+heu/hae]
28. Cachinillare=Chuckle, laugh a little [Diminutive of Cachinnare]

Friday, December 27, 2013

A New Generalized Function

There is a sort of mathematical function (technically a distribution) called a Dirac delta function, symbolized as \(\delta(x)\). This function has the property of being identically zero everywhere, except at the origin, at which point it is positive infinity, but in a specific sense. It goes to infinity in such a way such that the integral of the function over any interval containing the origin (but not as an endpoint), will be unity. That is, \[{\int_{-\infty }^{+\infty}\delta(x)dx}=1\]
An additional important property of the Dirac delta function is that, for any function \(f(x)\), \(f(x)\delta(x)=f(0)\delta(x)\). This is called the sifting property of the delta function.

A typical way to define the delta function involves the rectangular pulse function, defined as \[\mathrm{rect}(x) = \begin{cases}
0 & \mbox{if } |x| > \frac{1}{2} \\
\frac{1}{2} & \mbox{if } |x| = \frac{1}{2} \\
1 & \mbox{if } |x| < \frac{1}{2}
\end{cases}\]We then have \[\delta (x)=\lim_{a\rightarrow \infty} a \, \mathrm{rect}(a\,x)\]Notice that this would indeed have the required properties.
For fun, let us introduce two modified delta functions: a right handed and left handed one. We define these using the right and left handed rectangular pulse functions, defined respectively as \(\mathrm{rect}_R(x) = \mathrm{rect}(x-\frac{1}{2})\,,\,\mathrm{rect}_L(x) = \mathrm{rect}(x+\frac{1}{2})\). We would then have \[\delta_{R} (x)=\lim_{a\rightarrow \infty} a \, \mathrm{rect}_{R}(a\,x)\,,\,\delta_{L} (x)=\lim_{a\rightarrow \infty} a \, \mathrm{rect}_{L}(a\,x)\] These would have the same properties as the centered delta function, except that the sifting property becomes, respectively, \(f(x)\delta_{R}(x)=f(0^{+})\delta_{R}(x) \, , \, f(x)\delta_{L}(x)=f(0^{-})\delta_{L}(x) \). In addition, we can now better formulate the integral properties of the various delta functions. Let \(A<0\) and \(B>0\). We then have: \[
{\int_{A }^{B}\delta(x)dx}=1,\,
{\int_{0 }^{B}\delta(x)dx}=\frac{1}{2},\,
{\int_{A }^{0}\delta(x)dx}=\frac{1}{2}\\
{\int_{A }^{B}\delta_{R}(x)dx}=1,\,
{\int_{0 }^{B}\delta_{R}(x)dx}=1,\,
{\int_{A }^{0}\delta_{R}(x)dx}=0\\
{\int_{A }^{B}\delta_{L}(x)dx}=1,\,
{\int_{0 }^{B}\delta_{L}(x)dx}=0,\,
{\int_{A }^{0}\delta_{L}(x)dx}=1
Notice that, in every case, \({\int_{A }^{B}}={\int_{A }^{0}}+{\int_{0 }^{B}}\), as must be the case.

Suppose now we consider the opposite case: we begin with the rectangular pulse function, but instead of making it narrower and narrower and taller and taller, we make it wider and wider and shorter and shorter. That is, suppose we define a new function \(\eta(x)\) that also has unit total area, defined as \[\eta (x)=\lim_{a\rightarrow \infty} a^{-1} \, \mathrm{rect}\left(\frac{x}{a}\right)\] This function is the same as the uniform distribution function over an infinite interval. Oddly enough, this means that, for \(-\infty<A<0\) and \(0<B<+\infty\), \[
{\int_{A }^{B}\eta(x)dx}=0,\,
{\int_{-\infty }^{A}\eta(x)dx}={\int_{-\infty }^{B}\eta(x)dx}=\frac{1}{2},\,
{\int_{B }^{+\infty}\eta(x)dx}={\int_{A }^{+\infty}\eta(x)dx}=\frac{1}{2}\] This suggests some funny business going on at infinity: it seems the cumulative function is discontinuous at \(\pm\infty\).

The function also has some other interesting properties:

  • It seems to be a counterexample to the claim "for a function \(f\) identically zero everywhere, \(\int_{-\infty}^{+\infty}f(x)dx=0\)", as \(\eta(x)\) seems to be identically zero everywhere and yet has a nonzero improper integral. Furthermore, it seems that we cannot interpret its improper integral in the usual way, e.g. as the Cauchy principal value.
  • It is invariant under a finite translation, that is, \(\eta(x-a_{0})=\eta(x)\). This would mean that convolving a function with it would merely involve taking the inner product, that is, \(\eta(x)\ast f(x)=\int_{-\infty}^{+\infty}\eta(x)f(x)dx\).
  • Convolving it with another function (if the convolution exists) gives a constant function which with the value of the global average of the convolvend. That is, \[f(x)\ast\eta(x)=\lim_{L\rightarrow \infty}\frac{\int_{-L/2}^{+L/2}f(x)dx}{L}\]
    The resultant function is just the constant component of the input function. For instance, \[e^{-x^2}\ast\eta(x)=0\,,\,  \cos^{2}(x) \ast\eta(x)=\frac{1}{2}\]
  • It almost seems like the function could be represented by a pair of delta functions at \(\pm\infty\). Namely, it seems almost that \(\eta(x)=\frac{\delta(x+\infty)+\delta(x-\infty)}{2}\). However, this is not quite true.
  • The Fourier transform of the eta function can be determined by considering the limit of the transform of the rectangular pulse \[
    \hat{\eta}(\omega)=\int_{-\infty}^{\infty}\eta(x) e^{-2\pi ix\omega}\,dx=\lim_{a\rightarrow \infty} a^{-1}\int_{-\infty}^{\infty} \mathrm{rect}\left(\frac{x}{a}\right)e^{-2\pi ix\omega}\,dx\\
    \hat{\eta}(\omega)=\lim_{a\rightarrow \infty}\frac{\sin(\pi\omega a)}{\pi\omega a}=
    1 & \mbox{if } \omega=0 \\
    0 & \mbox{if } \omega\neq0

It is also possible to modify the eta function by making it right- or left-sided (as with the delta function).\[
\eta_{R} (x)=\lim_{a\rightarrow \infty} a^{-1} \, \mathrm{rect}_{R}\left(\frac{x}{a}\right)\,,\,
\eta_{L} (x)=\lim_{a\rightarrow \infty} a^{-1} \, \mathrm{rect}_{L}\left(\frac{x}{a}\right)
\] The properties are mostly similar (including translation-invariance, zero finite integrals, etc.). While the symmetric eta function takes the global average, the right-handed one takes the average over positive values, and the left-handed one takes the average over negative values. For instance, we would have \[\int_{-\infty}^{+\infty}\eta_{R}(x)\left(\cos^{2}(x+|x|) \right)dx=\frac{1}{2},\\
\int_{-\infty}^{+\infty}\eta_{L}(x)\left(\cos^{2}(x+|x|) \right)dx=1\]I'm sure there is more to say on this, and I will continue to look into the properties of this new, strange function.

Thursday, December 26, 2013

Reticaudicem Habemus (we have a blog!)

Hello World.

I have made this blog, basically as a place to air my thoughts and make more public what I happen to be working on.

I have a variety of interests, including but not limited to languages (particularly English and Latin, but also Greek, Italian, German, Spanish and others), etymology, mathematics, physics, and philosophy. I plan to write about each of these, though I suspect, at least at first, that I will have much of philosophy, particularly critiques of arguments for god's existence.

I myself have been an agnostic atheist for quite some time, and have for several years been interested in apologetics. Particularly, I have found the articulated and outspoken debates of Dr. William Lane Craig very informative, as to the arguments for god's existence and their defenses. I have since learned about other proponents of philosophical theism, and have become especially interested in the project of natural theology. I hope to interact with these arguments in upcoming posts.

In addition to this, I plan to give some of my musings on more general philosophy, as well as possibly some social and academic issues. However, there is much in the way of non-philosophy I also plan to give, such as some amateur work in mathematics.

Lastly, but importantly, there is much I have written in Latin that I hope to make public. Recently, I have become very interested in writing Latin translations of works in English. My main projects have been writing a translation of JRR Tolkein's The Hobbit (before I learned someone beat me to it, and before Peter Jackson decided to make a new trilogy out of it. I know, I'm such a hipster ). My other area of interest in translating has been poetry and song. Recently, I have translated several works of Dr. Seuss (though someone also beat me to that idea): I hope to post several translations over time, and hopefully add more.

Finally to explain the name of this blog: the name derives from the greek roots ὐπερ- (hyper-), a prefix meaning "over" or "excessive", and φρονειν (phronein) a verb meaning "to think". Thus, it translates to "over-thinking," which some would consider apt to describe me. Alternately, it can be translated to mean "beyond-thinking" or "super-thinking", which is a bit more complimentary.

P.S. As to the name of this post, I have attempted to bring some modernity to the Latin language. Others have proposed words for "blog" in Latin, such as blogis for "a blog" and blogire for "to blog". If I were to propose some words of this sort, I would opt for blogum for "a blog" and blogere for "to blog". However, to keep it more etymologically neat, I have opted for reticaudex, "net-notebook" (incidentally, caudex seems an apt translation of "logbook", as it can be translated both as "notebook" and as "tree trunk").
As for the verb, it seems there are several options: scribere in reticaudice "to write in a blog" is the most plainspoken way to phrase it , or scribere in interrete "to write in the internet". However, we may offer some contracted forms, such as retiscribere, or even (though hardly Latin-sounding) retscribere "to net-write". On the other hand, we may opt for simply introducing the adverb interretie "online" and say interretie scribere. I would be very averse for turning the noun itself into a verb and writing anything like reticaudicere, even if it is rather neat sounding.