2007/10/20

Dropalme

What can a poetess-biotechnologist and a scifi writer-physicist chat on? They can, of course, stray into mathematics, their common love. Excerpt:


Pratyu: well, you heard of Cantor?
Nirmal: No
P: George Cantor. a mathematician. pure math.
N: Ok...
P: he meets satan when he dies
N: I have not heard of him
Lol
And...
P: hmmm
satan tells him "maccha, i'll ask you some questions. you answer them i'll send you to heaven. else to hell
N: Lol
Go on.
P: 1. i shall have a natural no. in my mind.
N: ...
P: find it
N: ...
P: so cantor starts asking, 1? 2? 3? ............
somewhere he hits upon the one satan has in his mind
N: Ok...
P: 2. i'll have an integer in my mind. find it
N: ...
P: cantor: 0? + - 1? + - 2? + - 3? .........
somewhere he hits it
N: ...
P: 3. i'll have a real no. in my mind find it
N: Lol
Cantor loses voice
P: cantor: "maccha, my own theorem. between any two rationals there are infinite no. of rationals. between any two reals, infinite no. of reals... and stuff like that
not fair"
N: Ok...
P: ( it indeed is a very popular cantor theorem )
N: Yeah I know the proof too
Didn't know it was Cantor's
P: satan : fine. i'll have a pair of integer in my mind. find them
N: Can prove graphically
P: how would u go about if you were cantor?
N: The last question?
P: ya
no no
we are still in the middle
yes the last question
N: Oh I get the nuance...
P: hmmmmm
N: He must give it like a co-ordinate of a point
P: so how would you go about?
N: *the co-ordinates
P: yes...
yes....
N: H'm...
Why then he must fix x and vary y over all integers, and do the same for different x's...
P: true
N: Though I am sure this is not the answer sought
P: but cantor is smarter. so instead he starts covering squares on the plane. so first (0,0) (0,1) (1,0) (1,1)
etc
N: Oh...
P: this way he is covering in a better fashion and is safer and will probably hit faster
agree?
N: Oh!
One sec..
Yes..
P: nice. now satan says.. fine i'll have a triplet in mind
so now can you guess what cantor would do?
N: Cubes is the immediate answer I can give
P: correct
now here is the puzzle
N: And so on, is it?
Lol
P: the ultimate one
N: State away
P: satan will think of an ordered n-tuple
he won't specify n also
how to go about?
N:Very sweet of Satan, isn;t it?
P: he he. after all he is Satan
N: OK...
Square of area one, cube of volume one, four-D regular 'solid' of 4D volume one and so on...
Then do square of area four, cube of volume eight, and so on...
Then square of area nine, cube of vol 27...
I am guessing
P: hmmm...
infinitely long we might never hit him
N: Yes
P: his n-tuple i mean
N: Yeah
I found the flaw in my algorithm
h'm...
P: hmmm
N: Ok, did u crack it?
P: i couldn't so far come up with anything
poori said may be we could use vector algebra
N: H'm...
Sruthi knows the ans?
Or she asked in doubt herself?
P: no.. suman (elec) asked her
N: Ok
P: So that was it
N: Very nice...
P: Do you know that sania mirza beat Martina Hingis?
N: I must tell you something in return
O did she?
God bless her
Although I am a Hingis fan and not Sania's
Do you know about the palindrome conjecture?
Rather...
Palindrome Conjecture
P: me too actually
what is it?
tell me
hmmm
N: Ok..
Take some number
Two-digit
Suggest
P: 45
N: Well
45 is too easy an example
Anyway
Invert the digits
54
Add 45 and 54
P: ok
N: 99
Palindrome
P: 99
N: Take a three digit no. now
P: ooh
169
N: Reverse
961
P: plus 961?
N: Add
1130
P: ok
N: Reverse
311
P: 1441
N: 311 + 1130
Palindrome
!
P: yes
yes
N: Take another
Say..
476
Reverse
674
P: ok
N: 1150
Add 511
P: yes plus 511
N: 1661
Palindrome
P: 1661
ok ok
i get it
N: You will get a palindrome in finite steps
Take 196
And tell me in how many steps you get the palindrome
P: oh
ok
N: Please do it for me
P: ok
N: How many steps?
P: oh this is long one isn't it?
N: Yeah
P: hmm
N: People have tried for....
700 million iterations...
P: so am i to pack manual work and try a general model?
N: And are yet to get a palindrome
Computers have been running in vain for weeks together to get a palindrome
P: wooooow!
but what is the proof it always happens
is there an inductive proof?
N: There is no proof
Hence not the Palindrome Theorem
Palindrome Conjecture
P: ok conjecture
i c
nice nice


Notes:

(a) I am still in the dark re Cantor's problem.
(b) Saying 'God bless her' need not imply theism.
(c) '700 million iterations' was a shoddy mental estimate. The actual count ought to be much more -- 300,000,000 is the # of digits.
(d) 196 is the smallest of such adamant Lychrel Numbers. Check out its funny etymology too.
(e) The title of the post is, of course, a pal in Drome.

2 Obiter dicta:

Blogger Mohan K.V couldn't resist being opinionated thus:

Most fascinating! On a related note, I'm sure you'll find this interesting:

http://yet.typepad.com/round_dice/2005/09/the_god_of_smal.html

I wanted to put a blogpost about it sometime, hmm.

And next time you explain title fundaes, put them in rot13 :-)

9:46 AM  
Anonymous Lakshmi couldn't resist being opinionated thus:

Do you kids really converse like that? [Shudders]

9:12 PM  

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