A small review of some math apps on Android

Among the math apps, I can say MathStudio (very costly, but worth spending if you know how to use it) and MyScriptCalulator (No cost) are the best user friendly math apps available on Android. Though I have also installed Cctave, Maxima, Gnuplot & PariGP spin offs, but they work best as desktop apps.

MathStudio usage is almost like Mathematica (but nothing can beat wolfram Mathematica). It allows you to solve all kinds of mathematical problems from among vector/function plotting, indefinite integrals, differential equations, fourier transforms etc. But the best thing I liked about it is that it builds extremely neat 3D plots.

MyScriptCalculator allows you to enter simple arithmetic calculations in a natural way and then uses handwriting recognition to get you the answer (similar to an ipad app Pankaj showed me). I now do not use calculator until unless I have to do some form of conversion.

One can also use GeometryPad and Dr. Geo for teaching/learning simple co-ordinate geometry. Almost all functions are dynamic and parametrised.

For small simulation purpose, you can use octave,Maxima,Gnuplot & PariGP spin offs by writing small programs (can write huge simulations by attaching an external keyboard to tablet/Notebook). But they need to be configured properly.

An ode to flattery...

Our Lord's ears are great & it must be worshipped. There is but one truth, to worship his ears. The grooves, curves and the twists in his ears symbolise the great twist and turns of our lives. But the ultimate reality is, it all goes into a deep hole.

"O' Lord! please absorb our pains and sink it through thy veins."

The hole is the ultimate path to salvation; the more pain it causes, the more pleasure we get afterwards.

"Every year we must pierce our ears to get big tears,
& in great commune, pull each other's, to shed more tears,
then pray together & ultimately shed all our fears."

O' Lord let the blood of our ears satisfy your thirst, so that you may forgive us of our sins. Let you hear our pain, sorrows, sacrifices & offerings through your holes. For the hole is but only truth available to us.

"There is no other lord here, who can bear us to hear.
O' Lord, mighty creator of spears, one who kills with it,
the demon hoards, who come to our nears.
It is our Lord who is so humble,
one who drank our poison without any mumble.
The almighty must be adorned,
for he gave us all, with which we were all born.
For, it gives us tears when in joy with our peers.
Now he wishes to pull our ears,
for all our sins, disbelief & jeers."

Our Lord once said in his holy book that he might delay his incarnation on account of his delayed routine, owing to his prolonged hole cleaning, but the ultimate judgement will always be heard, because it is his holy ears, that we all bear. He has asked his believers to hear only what was said, because he has deprived us of all rationality. And those who fail to listen to his words, will always slip endlessly through his dark hole without any hope of resurrection, for the path for them is without light & goal, in the hole. Those who obey his will, pass through a shortcut and reach heaven, which is actually another hole, full of light & ultimate pleasure. And the reason why there are so many holes, is that, it is the only truth that is in existance. For holes make everything move and groove. Holes remind us of our limitations, for we slide through it with hope of salvation.

A review of Russian Movie Konets Vechnosti (based on The End of Eternity by Issac Asimov):

There are Eternals and there is Eternity, a temporal field in spacetime which exists through centuries. The Eternity was created in the 24th century and does employ best minds from all of the centuries since then. It was supposed to be eternal but beyond a certain future they are blocked by some mysterious power/force. And if they travel beyond these hidden centuries, they find Earth, a barren planet & humanity completely extinct. For eternals, who can watch all of the past(since the creation of temporal field in 24th century) present and future, by travelling upwhen & downwhen within the Eternity, the hidden centuries are a setback. They do cause reality changes and then watch its effects in the future. Their mission is to create a perfect happy time for all of the humanity by minimising their suffering in all of the times. But their own time proceeds in a normal manner, they do age, and it is independent of the true reality's time changes.

In order to be really eternal all of spacetime must be closed in loop to Eternity's temporal field, but they can't. They suspect that Timers, from the hidden cenuries, are fast catching up with them and want to destroy their power to change humanity's fate (a fate which they see fit). But what could the Timers be plotting against them, and why would they not let a guardian organization oversee all of humanity's welfare. Probably the answer lies in Eternity's decision to delay and sabotage space travelling capabilities of Humanity. The timers are themselves plotting reality changes to delay humanity's inevitable extinction at the specified time...but what kind of plot.

How I keep track of my bandwidth usage...

Since my current Internet Service Provider Reliance Communication has started cheating, I now keep an account of my bandwidth usage. Here's a script I use for every internet session:

filename: netusage.sh

date >>usage.txt
ifconfig ppp0|tail -n 2 >>usage.txt
ifconfig ppp0
if [ "$?" -ne "0" ]; then
cp usage.txt $( date | sed -e "s/://g" |sed -e "s/ //g").txt
rm usage.txt
sleep 180;
It takes a sample of usage every 3 minutes and when you are done, dumps your usage for the session in some file with name such as "SunFeb5044143IST2012.txt". Later you can grep, cut and sum all of your usage from all of the files for a particular period.

And if you are interested in some graph of your usage pattern, you cane even do that using some kind of regression or time series.

Other better ways are welcome.

A review of the movie "The Road"

"Are you carrying the fire" asked the little boy with the pointed gun. He dreamt of being a good boy, as all the boys at such an innocent age do. The world around him is brutal & harsh and it's slowly coming to an end. There is fear,scarcity (of food), cannibalism and above all no prospect of a stable future. The houses have all burnt out, plants don't grow anymore and the trees are falling. There is no sunlight and as the world is overcast by gripping shadow of cloud & fear all around, there are some who still carry the fire of civilization within. Probably a Human face in the light of adversity;"Are we still the good guys...we always will be no matter what happens","We would never eat anybody, would we...".

And as the boy and his father travel further south, scavenging through the streets, in the hope that it will be warmer there, they encounter various difficulties of survival. The boy is a soft meat and there is every chance that he will be eaten alive. Unlike the typical cannibal/mutant tamasha films of Hollywood (like I am Legend, Legion & Resident Evil) which are so unreal, these are real cannibals who are forced to eat their own kind to survive. Some of the surviving families have even built concentration camp style basements where they keep skinny but live people to be cooked and eaten later.

The father has a solution; he has saved two bullets, one for himself and one for his son. He has even taught him to shoot himself, when faced with no other alternative. But he is trying to prepare him; for a brutal & lawless society, where survival is the only purpose left. He still read him stories and upon his last breadth tells the boy to carry his gun & find good people...

A review of Battlestar Galactica

Battlestar Galactica: An exodus journey of surviving Humans, post apocalyptic/Nuclear-war scenario. into space/cosmos, also surviving from Cylons (AI machines), who now look and feel like humans & most of the times exceed their capabilities. The humans have lost their battle and all of the twelve human planets/colonies are completely destroyed and are occupied by the Cylons. But the lucky few, who were wondering the cosmos /space at the time of attack, survived the attack.

These 50,000 survivors, whose number are dwindling day-by-day, due to nasty Cylon attacks & plots, live in many spaceships. After the attack all of these spaceships assembled & formed a cluster around the sole surviving, old-generation, Battlestar named Galactica. These Spaceships have Faster than Light (FTL) travelling capabilities, and their route & destination is planned by Galactica's powerful supercomputers. The precise distance achieved in one jump is limited by the computing capabilities of the supercomputers. So greater distances are achieved in multiple jumps. But to make the matters worse, Cylons have infiltrated the human cluster, with their Agents among Humans, and have superior technology to compute at least 2 or 3 times the FTL distance, that the human technology could compute. Also on being dead a Cylon could upload/transmit his/her/its memory into a Resurrection Server and later be reborn with its intact memory but a new body of the same model who looked exactly the same.

Without hope, the Humans are on the run, and they sometimes fight back, with the sole purpose; survival into an unrelenting universe. The Humans have a small but an excellent fleet of fighter aircrafts and Fighter Pilots. But the fleet is losing their count in frequent fights with Cylon fighters and the replacements are hard to find.

Also the limited supply of water and mineral resources too dwindle very quickly. And hence Humans' major exploratory activities centre around finding water and mineral resources to satisfy their survival needs, instead of making an effort to find a suitable planet to survive biological life. The citizens are demotivated and susceptible to rumours & fears, while also being xenophobic to the possibility of Cylon Agents being among them.

But something is different. And while the humans are religious, who pray to the twelve Lords of Kobol, the Cylons too have found their religion in the form of one God.

But not all humans believe in the stories of the Lords of Kobol. The Lords are said to have made an exemplary journey, in the past, from a planet called Kobol, to the twelve new planets/worlds/colonies and possibly to a thirteenth mythical planet called the Earth. The religious text books of Humans are filled with prophecies and stories of these journeys. But some leaders of Humans find some resemblance in their current situation and some of the prophecies of their religious books. And so begins the search/effort/journey to decipher and retrace the path to the thirteenth mythical planet, which could sustain life.

But the Cylons too are interested in finding about the myth & the Earth. They could have left these decaying humans with their problems, but they didn't and Why?

An odyssey with toys

A day before yesterday I made a visit to a toy manufacturing company in Pune to gain some new perspective on the book I am currently writing. The company is known as Third Wave Scientific Products Pvt. Ltd. The place was quiet far away near warje flyover and took me about an hour or so to reach. So I arrived late, when they were about to close in just half an hour.

Nevertheless, I arrived at the reception and made some inquiry about the toys they manufactured. The lady at the reception handed me a catalog of the products and I started to have a look into it. To my surprise the products were extremely cheap. The same toys with some big toy manufacturer or of foreign origin would have cost-ed at least 3 or 4 times more. Although these were not the kind of toys I was looking for, I still marked a few of them I would look or buy, and handed the list to the lady.

Meanwhile, I overheard some employees, having a conversation, about creativity in toys, near the reception. So I intervened and started a random conversation about toys with them. And After a while, a few uncomfortable question, about how they decided what needs to be manufactured, and I was directed straight to the owner Mr. Suyash Dake.

The talk with Mr. Suyash Dake was quiet fruitful and I gained quiet an insight from this talk. We talked for about half an hour and it turned out that he quit his job at CDAC pune, in the year 1995, to pursue his passion for toys. Initially as a young man Mr. Suyash would collect garbage (testube etc.) from a chemist shop and the shop owner would consider him a crazy man. But later on he would call him before he threw anything. The young man would then experiment and create toys with this junk, which later grew into a passion, obsession and then a full-time profession. Well, this is what a real passion/obsession is all about, you just can't give it up no matter how crazy it would look to others.

Mr. Suyash told me that he currently cannot even fulfill 40-50% of the demand that he gets for his toys and opportunities for creative and educational toys are quiet immense. We discussed how bigger toy manufacturing companies are charging ridiculous prices for the toys which are not worth even 1/5 or 1/6 their price. Although his is a small setup and has an immense opportunity to grow at a faster rate than current, Mr. Suyash has made it a primary point that the toys manufactured at Third Wave are available at a low and affordable cost to anyone who has slight interest in experimenting with scientific concepts. Most of these toys are directed at schools and school level kids.

Then, he even showed me some of the publications he reads on toys; a research thesis on toys submitted at IIT Bombay long time back, some books on scientific toys by Vikram Sarabhai himself and some other foreign publications. Since he did not have an electronic copy of any of these, he offered me to get them photo copied, which I would do on my next visit. We also talked for a while about a few interesting toys, about my book and some other topics. And then after an exchange of email and phone number I said good bye to him, bought a few toys at the reception and left.

Then I headed straight for M G Road. I reached the place and started walking uphill and made stops at two different toy shops to look for new & interesting toys. During this trip, I came across two interesting toys which I was not previously aware of.

The first one is a metal puzzle, in which a number of two similar (sometimes dissimilar), thick metal straight & curved wire pieces are inter-linked together and you are supposed to unlink them. You can't bend these pieces with strength and the only way to unlink them is to rotate and move them in various spatial configurations. Although many a times it is frustrating trying to unlink them, it has a good lesson to teach in terms of spatial understanding. We are all accustomed & hard-wired to straight edges and orthogonal angles of euclidean geometry. But then, when we are presented with curved spaces and angles this common sense knowledge fails & forces us to think and conceive a new idea about the space itself. This toy can act as the beginning of that notion, although there is more to geometry and space than just this. I am also thinking, whether this toy has more to do with Algebraic/Geometric topology or knot theory than first meets the eye. I will do some more exploration/research on this and then write my findings later.

The other toy is called "fun linkz", which is looks like a less programmable version of geo-magnets in linking and non-magnetic. Only, geo-magnets have fully free 6 degrees of freedom around the linking points and this one has special linking ball which is a bit restrictive in free movements, although still with 6 degrees of freedom, owing to the two separately rotating hemispheres. And each hemisphere's linking can only be done in a (2 dimensional) plane with a slight 3rd dimensional orthogonal distractions. Other connectors have only 3 degrees of freedom in a (2 dimensional) plane. Although even this toy is fun, but I am a bit disappointed with the way these linking points are made & can not preserve a perfect mirror symmetry while linking two objects. It's like linking two books head on, with same number of pages, page by page, with alternate pages from different book. But I guess any kind of perfect symmetry is harder to find even in nature.

About ibus-table-mathwriter

This blogpost was long pending and is about ibus-table-mathwriter (earlier known as mathwriter), which I had first written for iiimf. Last year I ported it to ibus-table and did a major update in terms of mathematical symbols. Though it is not fully complete yet, it is in such a state that it can be used conveniently.

The ibus mathwriter table lists the key-map in the following form:
<key-sequence><space/tab><Unicode math symbol><space><frequency>

The <key-sequence> is the sequence a user enters in order to input <Unicode math symbol>. Since the table uses ibus-table engine, all partial inputs are look ahead and possible results are presented as possibilities.

Now either the user selects any one of these possibilities or either he continues to enter more characters from the sequence or writes the sequence completely. One good thing about this table is that there are mostly more than one way to enter a particular math symbol. Either a user can use a more descriptive key-sequence (almostequalto for entering ≈) or use logical shortcuts (~~ for entering ≈).

Words in descriptive key-sequences are either (partially or fully) separated by _ character or otherwise all words are merged together. For instance almost_equal_to, almost_equalto and almostequalto are equally valid for the value ≈ .

Whereas, Logical shortcuts are faster to input and sometimes very intuitive. It's a matter of getting used to them. They make use of the following three principles

1. Principle of lookalike: The characters can be formed with approximate lookalike input sequence.

2. Principle of rotational transform: Lookalike sequences are pre-fixed or post-fixed with |_ or _| or __ to rotate rest of the sequence (partially or fully) by 90 degrees or 180 degrees. Prefix rotates post-sequence, to lookalike, in anti-clockwise direction, while post-fix rotates pre-sequence, to lookalike, in clockwise direction.

3. Principle of lookalike input line/curve sequence : Though the character looks nothing like what is intended, the input sequence uses similar sequence of lines and curves in the actual shape (e.g benzene, ⏣, can be input as |/\|/\ or /\|/\| etc.).

However one rule common to these three principles is that all sequences can only be formed from the keys available on a standard keyboard.

For example in order to enter a ∠ (angle)character a user can either write angle directly or enter the key-sequence /_ . Since ibus-table does not allow = character in input sequence we have used -- wherever it is required. Here are some other examples in the form

<key-sequence><space/tab><Unicode math symbol>:

lookalike Examples:

angle_right ∟
angleright ∟
|_ ∟

_|_ ⟂

centimeter_square ㎠
centimeter_2 ㎠
centimetersquare ㎠
centimeter2 ㎠
centimeter^2 ㎠
cm2 ㎠
cm^2 ㎠

circle ◯
() ◯
O ◯
(+) ⨁
(-) ⊖
(-) ⦵
(-) θ
theta θ
(x) ⨂
(*) ⨂
(/) ⨸
(%) ⨸
(/) Ø

(+ ⨭
(x ⨴

(.) ⨀
(.) ◉
(o) ⨀
(o) ◉
(()) ⦾
(o) ⦾

emptyset Ø
nullset Ø
(/) Ø

Since we cannot have special logical shortcuts for ⫝̸, because nothing looks like it, we prefix |_ in the user input sequence (for anti-clockwise 90 degree rotation) (-\-, which then looks like what is intended. And hence the key-map becomes

|_(-\- ⫝̸
|_(-\ ⫝̸
|_(\- ⫝̸
|_E\- ⫝̸

while some other possibilities for the same,

forking ⫝̸
\|/ ⫝̸

or post-fix _| to -\-). And hence the key-map becomes

-\3_| ⫝̸
-\)_| ⫝̸
-\-)_| ⫝̸
\-)_| ⫝̸

similarly __ (two underscores) is pre-fixed/post-fixed to rotate some (partial or whole of) shortcut to 180 degrees, which is lookalike to some Unicode math symbol. For example:

thereexists ∃
__E ∃
!__E ∄
__U ⋂

more examples:

root4 ∜
fourthroot ∜
\4/- ∜

^2 ²
^( ⁽
^r ʳ

__C-- ⫆
-x- ⫘
__C-C ⫘
|_-3- ⫛

largelefttriangleoperator ⨞

<| ⨞
< <
<_ ≤

<- ⇐
<-/- ⪉
<) ⪦
<() ⩹

<. ⩹
?< ⩻
<< ⪡

log ㏒
ln ㏑

/_\ ⩟
/\_ ⩟
_/\ ⩟

/\\/ ⩙
\//\ ⩙
X ⩙

-\-/- ⩝
\-/ ⩝
-\/ ⩝
\/- ⩝
-\/- ⩝

||- ⫦
||-- ⫦
|-|- ⫦
|-|-- ⫦

+- ±
-+ ∓

/-\ ⨺
/x\ ⨻
/+\ ⨹

[.] ⚀
[..] ⚁
[:] ⚁
die3 ⚂
[.....] ⚄
[::.] ⚄
[:.:] ⚄

T| ⫪
|T ⫪

||-|| ⩎
||^-|| ⩎

benzene ⏣
|/\|/\ ⏣
/\|/\| ⏣
\|/\|/ ⏣
|/\|/\ ⏣
/\||\/ ⏣

|\ ⨡

I think, the above mentioned (random) examples would help to explain the concept behind ibus-table-mathwriter. Please accept my apologies for not being too rigorous currently. The application is experimental and still evolving. But I guess I have conveyed the idea behind it.

The ibus-table-mathwriter package is currently available as a part of ibus-table-others package on fedora. There is no user manual and you can use the key-map table to get used to the shortcut lookalike sequences.

Also, if I get some time, I will soon fork from ibus-table engine to make a specialized mathwriter table engine and enhance the concepts which would otherwise be not possible using current ibus-table engine.

Suggestions are welcome.


Teaching Mathematics by associating it to religious texts...

Here is an excerpt from an article by C Musili from a journal "Selected Articles from Resonance- A journal of Science Education: Mathematical Analysis" of Indian Academy of Sciences:-
One of the exciting characters in the epic Mahabharatha, one that has fascinated me most since my childhood, is Nakula (the fourth of the Pandava brothers). Especially intriguing was his ability to travel in rain on a horse, without getting wet. Generally speaking, not everyone is aware of this great skill of Nakula as against the common knowledge that he could tame and train any kind of horse to any degree of perfection. None of the host of Sanskrit or Telgu pundits/scholars I asked over decades, could offer a plausible explanation. In fact, most of them looked surprised and wondered why I was seeking justification instead of leaving it aside as the product of fertile imagination!

In this article, I would like to present a simple mathematical model as a possible motivation based on which Veda Vyasa might have attributed this extraordinary talent of Nakula. This will of Course imply that Veda Vyasa was a mathematician! Surely. Why not? Even an applied topologist for that matter!

The Model

Assume that rain is falling on the floor sharply at points both of whose coordinates are rational numbers (with respect to a chosen set of coordinate axes). This means that it is raining rather densely. The simple theorem in topology about the arcwise connectedness of the complement of a countable subset of the Euclidean space ℝⁿ (n≥2) {R^n (n>=2) for Unicode disabled} now implies that Nakula (shrunk to a point) can travel continuously from one dry point P to another dry point Q without getting wet. In fact, he can even travel smoothly, for example along a suitable arc joining P and Q. There are uncountably many such circular arcs joining P and Q, implying that the choice is indeed abundant......


So on and he continues to explain Real Numbers, Countable & Uncountable Sets and so on....

Similarly, can an annotated Mahabharatha (or any other old religious book) or even books like Harry Potter, be written with mathematical annotations to miracles/magic performed (or rewrite the book entirely). Surely subjects like Geometry, Topology, symmetry, Limits, Continuity, Cantor sets, Real & Complex Analysis etc would find its use there. We can only hope, probably this would inspire a few to take up subjects like mathematics & other sciences...

Journey of a Hacker...

Uphold thy ingenuity,
thou shall be rewarded.
Oddment restored,
distress parted.
Thou see a lambent source,
which leads to a distant course.
Climb thy soul on a ship,
& sail to the distant deep.
It is on this journey, that you will see,
what life holds for thee.
The treasure does not lie low, ashore,
for it is on the go.
Strive hard & survive the waves,
for pearls are on this way.
Steady thy captain, steady thy soul,
for we have yet to reach a goal.
The goal is an illusion to keep one tenanted
& thou shall not be cemented.