Round The Table - Discuss

Friends,

Here is something to warm the cockles of your heart:
What This Airline Did for Its Passengers Will Make You Tear Up - So Heartwarming - Heartwarming Video



L, Kamla

 

The psychedelic mushroom thing you posted Uttaraa has freaked me out and I have been deliberating on that from the day I went through the information, more so when I read in wiki under "Spiritual and well being"! I have been eating the brains out of all my friends who are extremely spiritual!

Also one of the programs that we like watching is Stan Lee's superhumans on history channel Stan Lee's Superhumans - Wikipedia, the free encyclopedia While I am quite taken with the physical capabilities, it is the mind ones that fascinate me and intrigue me.

JAG, thanks for that link - fabulous and loved it!

 

Wooohooo.....am I glad that KKrish is here in this class room or what...
lets head to those back benches ..Satchi u listening girl?
PS I was more "keep the novel" between the text book kinda girl....but dozing seems more appealing now

 

Hey dinny..link doesnt seem to work.

 

You are not the only one who refuses to assume things!
Newton & Leibniz used an infinitesimal approach in developing the calculus. When they devised it, they did not rigorously define what an infinitesimal was. They simply assumed it to be an arbitrarily small quantity, as small as you want it to be! This was very difficult for mathematicians to accept. Leopold Kronecker was against infinitesimals, since they were not 'defined'. So you are not alone!

When you refer to the 'epsilon' you are talking about the epsilon-delta definition of a limit developed by Bolzano, Agustin-Louis Cauchy & Weierstrass. The interesting thing is that this rigorous definition, that was probably taught to you in high school, was not fully developed until the 1820s - a full 150 years after the invention of calculus by Newton & Leibniz! The point is that it took the field a century and a half to develop ideas that are taught in beginner's calculus! A 150 years of intellectual struggle and controversy are compressed into two hours beginning with: "Kids, we are going to talk about limits today. Now, a limit of f(x) as x tends to a, is equal to L iff for any epsilon greater than zero, there exists a delta such that ......" Hey, hey, hey, wait a minute where did all that epsilon and delta come from?? The approach is subtle, not difficult, but subtle. It is taught very badly, without developing an intuition for the idea of infinitesimals! It is simply a rigorous formulation of "it can be as small as you want. You pick how small. Pick a small number, I'll show you that the limit is closer than that. I can do this for any small number you pick, no matter how small!" That's it.

Another interesting historical point is this: a formal, rigorous infinitesimal approach to calculus (i.e a rigorous version of the ideas Newton & Leibniz developed informally, without mathematical rigor) was developed ... guess when? In the 1960s by Abraham Robinson!! 350 years later!

So, it is not surprising that many students get lost in calculus. It is taught badly, presented as an 'obvious' finished product without all the controversy and quarreling that went into understanding the nature of mathematical proof.

More later!

PS: A high-school level treatment of Robinson's ideas is here: Infinitesimal Calculus.
Calculus: A Liberal Art is a very useful historical treatment of the ideas of calculus.

 

Dear Soka....You are simply unbelievable!

L, Kamla

 

Not again....
okay I have a better idea.I am gonna paste the the article here.




"Immortal" Jellyfish Swarm World's Oceans
Ker Than
for National Geographic News
January 29, 2009
A potentially "immortal" jellyfish species that can age backward—the Benjamin Button of the deep—is silently invading the world's oceans, swarm by swarm, a recent study says.

Like the Brad Pitt movie character, the immortal jellyfish transforms from an adult back into a baby, but with an added bonus: Unlike Benjamin Button, the jellyfish can do it over and over again—though apparently only as an emergency measure.
About as wide as a human pinky nail when fully grown, the immortal jellyfish (scientific name: Turritopsis dohrnii) was discovered in the Mediterranean Sea in 1883. But its unique ability was not discovered until the 1990s.
How the Jellyfish Becomes "Immortal
Turritopsis typically reproduces the old-fashioned way, by the meeting of free-floating sperm and eggs. And most of the time they die the old-fashioned way too.
But when starvation, physical damage, or other crises arise, "instead of sure death, [Turritopsis] transforms all of its existing cells into a younger state," said study author Maria Pia Miglietta, a researcher at Pennsylvania State University.
The jellyfish turns itself into a bloblike cyst, which then develops into a polyp colony, essentially the first stage in jellyfish life
The jellyfish's cells are often completely transformed in the process. Muscle cells can become nerve cells or even sperm or eggs.
Through asexual reproduction, the resulting polyp colony can spawn hundreds of genetically identical jellyfish—near perfect copies of the original adult.
This unique approach to hardship may be helping Turritopsis swarms spread throughout the world's oceans, she added.

Hold on...
did I land amongst the think tanks of IL??? :shock: faintingsmiley
Escaaaaape.....bie1

 

Ha Dinny, you beat me to it!

Here is a video clip on the same subject :
the 'immortal jellyfish,' Turritopsis dohrnii - YouTube

This is fascinating and I cannot imagine what wonders it will work if the process could be used to produce stem cells in humans to cure diseases such as cancer or spinal cord injuries etc. Let us hope there is some successful research not too far away in future!

L, Kamla

 

Fascinating Jellyfish, but it's an invertebrate.
Here's some cool natural weirdness in sharks (virgin birth!).
Stress conditions can produce all sorts of survival work-arounds!
Mammals can't do this naturally, but here's some engineered weirdness in mice!

 

Dear Kamla,

Please read post # 88 above and you would know that the stem cell research and cure for cancer is happening in the town I live in the US.

Viswa