“A man is rich in proportion to the number of things which he can afford to let alone.”
- Henry David Thoreau
Is being rich only about money? Don't we let go off what is not essential or important to us, even if we do not think about doing away with them willfully? Skin sheds.
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And here is a smile for today, a wry smile:
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Got this in my inbox...thanks, Sanjeev
World's first $1B home can't just be about flaunting wealth among the world's poorest. There is more ... than meets the eye.
ReplyDeleteThere is a notion in topology, the so-called homeomorphism which categorizes objects based on certain attributes. Objects that preserve these attributes under a given transformation are said to be homeomorphic. Consider two objects An (Antilla) and Py (Pluck Yew) and a transformation Th (tilted head), which when applied to An yields Py or Th(An)->Py. We say, An and Py are homeomorphic under Th.
"Mathematics is not the study of objects, but instead, the relationships between them"
Henri Poincaré ... which is said to have led to the famous Poincare Conjecture
Anon,
ReplyDelete"Mathematics is not the study of objects, but instead, the relationships between them"
Sounds cute I don't think this is true. Solid Geometry which is about the 3-D properties of objects by themselves. Mathematics is about representing the real world in the form of numbers and squiggles (also called "notation", like +, - , for example) and then make conclusions in squiqqle-land, and then apply it to the real world back again. Representing an abstraction of the real world is what creates new branches of mathematics over time.
-Al
It often turns out the it is physics that drives the need for new forms for mathematics, rather than the other way around.
ReplyDeleteIt is electrical field theory that resulted in the invention of notation for vector fields. Pure mathematicians like Ramanujam (number theory) or Galois (field theory) had to invent new ways to represent what was going on in their heads when they came up with their notation. Leonhard Euler was one of the most prolific in terms of inventing completely new branches of Mathematics...but as someone said "everybody stands on the shoulders of those before them"
-Al
The word "objects" in Poincare quote refers to abstractions, not necessarily real-world objects, and most certainly not confined to 3D. Indeed many mathematical objects are n-dimensional, a far cry from the real-world 3D. I won't burden mathematics with solving the "real world" problems. The opposite seems more plausible.
ReplyDeleteAnon,
ReplyDeleteYes, I get the sense of the statement...but I still object! :-) I agree that mathematics exists by itself and all, but if it did not actually help humans understand the universe, it would have just become a quaint intellectual construct by itself, propped up in a corner to be admired by professors during lunch breaks.
Overusage of this word Object makes sentences like the one by poincare senseless, and I am pretty sure it is not Poincare's fault.
Today, a word like "object", sounds like the word "system". Its overuse makes its usage very confusing.
I mean, I can say something like "The main object of this system is to systematically serialize access to the objects in the System in an objective and systemic way" and have someone nodding their heads in some given context where all of this makes sense.
-Al