### 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:

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 :-)

Do you kids really converse like that? [Shudders]

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