Droid: General, there is an incoming ship.
Grievous: Scan it.
Droid: We're detecting high levels of *sass on board.
Grievous: *slams fist Kenobi!
The best show of my growing childhood. Asking dad to allow us (me and my brother) to watch the show back in '08 late at night, and the hurriedness with which we used to finish our all food and chores up, before the show started, Oh! I seriously miss those days. A show, important part of my life, an inspiration. This show was totally a class apart.
May the Force be with you!
Math. The dreaded word.
Everyone seems to hate math. For its unintuitive! It’s like, math doesn’t give a damn what we think is possible, or what we think is absurd. Math does exactly what it wants to do, because that’s all it can do. We may not always understand it, but sometimes, once in a blue moon, we get a peek behind the curtain. Once every few hundred years, we can prove that cicada mating rituals are related to weather on Mars, and briefly glimpse the universe in its true glory.
But what if math is not math, but really everything? What if physics is math? Like just maths?
Consider Monstrous Moonshine.
Pretty, Isn’t it?
Monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. (*Wiki)
Professor Richard Borcherds of Cambridge University was awarded [August 1998] the Fields Medal, the mathematicians’ equivalent of a Nobel Prize, for proving a highly abstruse result in number theory called the moonshine conjecture.
It seems it was given this name because it was based on a coincidence between a result in number theory and the number of symmetries in an exotic concept called the Monster object. It was thought so unlikely that two such distinct areas of mathematics should have anything in common that the conjecture was described as moonshine, and the name has stuck.
Professor Borcherds was quoted as saying, “I was over the moon when I proved the moonshine conjecture”, a nice conflation of two of the common evocations of the Moon in the language.
Moonshine originally meant the same as moonlight. In A Midsummer Night’s Dream, Snug asks whether the moon will shine the night they perform their play, and Bottom replies in a brief panic: “A calendar, a calendar! Look in the almanack; find out moonshine, find out moonshine!” It still has this literal meaning in poetical or elevated contexts but we no longer use it in that way in daily life, unlike the matching sunshine. Instead, it commonly means something insubstantial or unreal, and so foolish or visionary.
It is now known that lying behind monstrous moonshine is a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, having the monster group as symmetries. This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge between two mathematical areas.
This makes me wonder, what if physics is also a part of mathematics?
Read this paper on On a Final Theory of Mathematics and Physics. Maybe it’s true! Worth a read.
Some Musings on Life:
There are only two tragedies in life: one is not getting what one wants, and the other is getting it,” said Oscar Wilde , the famous Irish playwright, novelist, essayist, and poet. We feel extremely sad when we fail to achieve something which we desire a lot. However, even those people who achieve their heart’s desire fail to live happily ever after as often shown in movies.
It is true that most students who desire to become an Engineer, wish to get into IIT to realize their dream. However, hardly one in a 100 realize their dream of getting into an IIT. Even those who get into IIT don’t get the choice branch and feel unhappy.
I had a colleague whose son got IIT-JEE (Advance) rank of around 200 a few years ago. Even he was unhappy because he could not get CSE (B Tech) in IIT Delhi and he had to accept the dual degree programme of CSE in IIT Delhi.
One of the greatest tragedies of all IITians is that they are too brilliant to fail in written examinations. Many of them get into IIM or do MBA/MS from a foreign university. They can easily get great jobs in corporate or government which ensures them a decent life and a respectable position in society.
However, this security of the job becomes their greatest hurdle when it comes to taking risks and become leader or an entrepreneur. Most IITians end up becoming just managers of top leaders. You would hardly see an IITian leading the country in politics, business or art. These top leadership positions go to such people who could not make it into an IIT.
If you list the top 100 most influential people of India, you would hardly find any IITian in the list.
Hence, if you are not an IITian, you must not be disappointed.
It is wisely said, “When God closes a door, he opens a window.”
Find out the window left open when your doors of IITs are closed.
There lies your path of success, happiness and glory.
(*Taken from a Quora Answer)
((It’s kinda like a book). A good place to look for, it’s somewhat comprehensive.http://neuralnetworksanddeeplearning.com/
I have always wondered, whether math is really necessary for understanding Biology. This question had eluded me since my high school when I took Math and Biology both as my elective subjects.
When I see this question raised again, I think I have an answer. Math is not essentially needed to understand Biology. It is useful and may be helpful sometimes, but that’s about it. You can get away with understanding math. You can learn to do the math if necessary, but you can escape the chains of “understanding it.”
Biology as Wikipedia states is “a natural science concerned with the study of life and living organisms, including their structure, function, growth, evolution, distribution, identification and taxonomy.” It is incredibly broad and rich, as the organisms themselves. When we’re talking about such highly complex systems, systems like millions of cells coordinating among each other, systems as big as thousands of organisms interacting and living in an ecosystem, can such diverse systems be described by just some set of equations?
The key even attempting to writing those equations is having an understanding of the system, an intuition what exactly is happening inside. Mathematics is just a tool, which is making our lives easier, giving us new numbers. But what these numbers mean requires an understanding of the system.
Mathematics is a tool. Sure, there exists complex mathematical formulae and domains like topology, number theory, but do we really need these? Basic math, standard calculus and statistics that we did in high school is more than enough to cover almost most of the math one would need in their Biology research. Understanding bio may require these two topics at some point, but that is all that one would need. And even these make their way into topics like Ecological studies and population dynamics, and a little bit in kinetics/metabolism, but sure you wouldn’t need these in Molecular Biology!
Consider Mendel’s Experiment in Genetics. His discovery of laws of inheritance relied on him spending 12 years in a pea garden, “observing”, making careful observations, and coming up with the classic Mendelian experiment that’d uncover the laws. He later came up with the law of independent assortment, which was a result of him realizing the progeny in a dihybrid cross coming up in the ratio 9:3:3:1 was just a result of his understanding and basic probability.
It was his careful observations, understanding, and his deductive reasoning. The math he used was just probability ( Something along the lines of “probability of a head showing up on a fair coin’s toss”; if you got 1/2 you’re already good at it!)
Even the principles of Evolution by Charles Darwin were a result of pondering over the dynamics of an ecosystem worked, principles that lead to the survival of the fittest. Mathematical formulations came later, but the true manifestation of Evolution was stated in the principle, not in the math.
These and many other examples just speak one thing that understanding and having a physical feel of the problem, of the system to which it is to be applied.math is a powerful tool, but only a tool nonetheless. You can come up with hundreds of equations, highly sophisticated models but it wouldn’t matter unless you can interpret what the results mean. What do these numbers imply?
“You don’t need Math to understand Biology. You need biology to make sense of the math, the numbers.”