The method of Lagrange Multiplier ! Optimize multivariate functions. Reply

Yesterday I learned the beautiful method of Lagrange Multiplier, to find the minima or maxima of multivariate functions. eg

If I ask you what’s the minimum value of a function, f(x,y) = xy, subject to the constraint 5x-y = 4, the answer would be -4/5. The method is this. Ensure that first-partials of function f(x,y) exist. That is fx = (∂f)/(∂x) is not zero, and fy = (∂f)/(∂y) is not zero. Else method won’t work.

For the given example the f(x,y) = xy, because fx = y and fy = x, our method will work.

According to the method, we have 3 equations:

(1) fx + λgx = 0

(2) fy + λgy = 0

(3) 5x − y = 4 More…

How to recognize words in various languages … a magic formula 1

1. the languages are “read” into Roman. Roman without any particular rules not defined is arbitrary. That is it becomes neutral, devoid of biases from language rules. It unlocks the languages into their neutral forms.

The languages are basically a rule or lock defined to capture particular meanings from a vast arbitrary tract of phonetics and noise. eg roman: t corresponds to 4 locks in Indian Language system and two locks in Japanese. t as in tatami, t as in taberu are the soft t and heavy t in Japanese. But in Indian t as in tumhara, t as in tenis, t as in thoda and t as in beithak are 4 different locks, 2 soft and 2 heavy.

But in Roman they are all but t. Note that English is not Roman. English is simply a hidden phonetics where you know what the lock is, but you do not show it explicitly. eg time is English, but in Indian lock its thaim, with t in thaim same as the t locked in beithak. More…

Comparing Hiragana and Indian alphabet ! 1

Indian Consonants have an internal vowel, a, not present in Hiragana [Japanese native alphabet]. This is also true in Katakana. [Japanese alphabet for imported phonetics or non native words]

That means 39 base consonants (of India), will be all said in a different way, which could not be accommodated by Hiragana or Katakana. So, I think this is just one vowel more, for Hiragana.

The Hiragana a is actually an abbreviated aa of Indian sound-base.

The other differences from Hiragana are how {hu, fu} are said the same way, but note that, in the alphabet itself {hu, bu, pu, fu} are a set of degenerated consonant and also so in Indian system. That means for hiragana these elements are simply similar and this fact reflects with the same symbol denoting the 4 elements, with small difference accommodated More…

Insight on killing self ! Reply

Consonant; what you say.
Vowel; how you say that.

eg K is consonant, in ki, ke, ka, ko, ku K is whats fixed, because that’s “what” we say. But “how” we say it varies; u or a?

Now why this flashed? I was checking a Japanese word: “jigai” (自害) which means suicide. This word comes from two bases: “ji” 自 and “gai” 害. I remembered “ji” is life.

(from my research years ago, I had realized plenty of such Japanese words having exact same base with Indian words or at-least the single or double consonant = “what” matching, with the variation seen in only, vowel = “how”)

So “ji” is one example of exact matching. Say how? Ji is in Jivan, Jina, Jinda More…

How equal is a conserved quantity as-before-as-now. Reply

For just a little sharing instead of writing voluminously on a blog that no-one (including myself) has a time or will to read.

When we say something is conserved (in Physics) we mean to say they are EQUAL as-before-as-now. Just how equal?

Classically we would claim exactly. But classical mechanics is a dogma held for too long. We know now its quantum mechanics that rules the roost (and eats it too, and claims its tasty even if cooked by itself)

So classically there is something called symmetry. A symmetry is like this. You do something to something else and yet certain property of that latter did not change. That idea of non-change is conservation. The idea that such a thing is possible is symmetry. eg you stand in front of the mirror. You notice that its you, although your nostrils are flipped and so on. But overall its you. eg not someone else. eg while the mirror changes certain direction of yours (left hand appears on right and so on) OVERALL its you and mirror does not change the identity of yours.

Here conservation corresponds to Your Identity, which is overall conserved (unless you take a very bad mirror). Symmetry is the fact that the property of identity remains intact. (also called beauty because the amount of beauty isn’t affected by mirror, just kidding, but certainly your beauty content isn’t changed much by plain mirrors. ) and Transformation (or certain changes that are allowed) is the way light is taken in a backward direction to form your image. (in Physics its called space or parity transformation)

That’s all a classical concept. In other-words an overall, big sized process. But in reality there are an infinitely large dimensions in which changes are taking place. And some changes are not symmetry (or your identity is lost or modified, due to the subtle nature of reality)

So due to this subtle and complex change (in so many dimensions) non-symmetry or loss of beauty or loss of symmetry doesn’t necessarily show up on a perceivable scale. While overall conservation might be there, some of it might be lost.

Equal as-before-as-now is merely an overall ideal and conservation and symmetry are not very precisely equal. This is a result of multiple (as many as a huge number) possibilities and multiple changes to subtle properties and subtle invalidity of reality.

The above is also what reflects itself as whats called spontaneous symmetry breaking. (although in mathematical and physical calculations it results from much deeper and advance logical frameworks of understanding) …

The Singapore maths puzzle. Reply

Now that I could lean back I guessed the answer for this puzzle after reading it a couple times mindfully. I think the answer is August 17. WHY? I will explain in detail. But first of all the answer I came across here (in NY Times) is obviously misleading and incorrect. They give July 16 as the answer, but their method is wrong because they eliminated both May and June and there isn’t enough information for such a step. What they should do is eliminate May 19 and June 18. Because these two dates (18, 19) are not duplicated in the list of dates.

Once they did so it would be clear from the conversation between Albert and Bernard that June 17 could also be eliminated. Because since Albert knows that June 18 and May 19 are not good candidates for DOB, neither can June 17 be. If June 17 was the date he would not claim “I don’t know the date of birth” because he already knows the month and there is only one date in this month that is June 17. More…

Are younger generations opposed to Capitalism? Reply

Are younger generations opposed to Capitalism? This is a guest post by Sabuj, who writes with much clarity on Quora and I thought this is interesting enough to be shared on this website. He also writes voluminously about various issues of his interest. Since he is very young, it throws a particularly refreshing view into limelight and I would urge you to read this and comment and importantly share this if you liked this. I also invite anyone interested to make a wider audience of his/her interests in creative writing connected to academics (such as science, philosophy, history and sociology in regards to science, cutting edge research and conceptual innovations etc but this is not to say this is the end of the list) can send me a link of his/her article or email me the write up to I would be glad to publish it here if its devoid of any basic concerns and encourage you to suggest a good writer of science, sociology, philosophy etc to contact me, who wants to write here occasionally or regularly. This is not a paycheck generator so you may as well get an unhindered interface to the wider world. (No its not a commercial website as of this moment or any closely seen future ) Its sole aim is to bring the new and fresh to the widows of the inspired world.

Here is Sabuj’s Article. I hope you all enjoy it.

Let me answer this as someone from the “younger generation”. To begin with, your assumption is incorrect. Today’s generation is not completely against capitalism – at least not against the spirit that an individual should be able to benefit economically in exchange of and in proportion to his/her services to the world. We couldn’t even dream of the revolution in information technology and software engineering without capitalism. I am sure your friends do use the products and services which are the outcome of capitalism for the ease of their lives, even though they may be critics of capitalism itself. More…

A new Physics theory of life ! Reply

A new Physics theory of life (linked)

2nd Law of thermodynamics and life connection.

The disordered systems do not exclude the formation of organizations, patterns and order in both life and inanimate matter. The 2nd law says there is a arrow of time OR; the favorable processes are the ones that go in the direction of increase of disorder or entropy. But there is a tiny favor that allows self replication or pattern formation etc as long as the dissipation of unwanted energy is possible to the external surrounding. By being in equilibrium with the external systems such as ocean or favorable heat reservoirs the matter or life-elements can replicate and order themselves and dissipate unfavorable energy. Hence life is possible and 2nd law does not eradicate the possibilities of life as long as such self replications are possible.

Given large amount of time the possibilities materialize .. so who knows monsters can form themselves in volcanoes given enough deal of time for them to come with their favorable self generation.

The arrow of time also explains why life is a slow process. Because the likelihood of such self organization to drive away disorder is really small. It needs billions of years, there is no God’s hands but mere natural selection and dissipation driven self organization.