Hard Drives with Lifetime Warranty

I wonder how much of a price premium people would be willing to pay for a hard drive with a lifetime warranty?

glimpseindex fun

Indexing 149,000 mail messages totaling 1.21 GB took 7 hours with glimpseindex -o. The total size of the .glimpse_* index files is 368 MB. After bzip2 compression, the messages themselves are 420 MB and the index files (surprisingly) compress by 50% to 182 MB.

Circle polygons

What are polygons all of whose vertices lie on the circumcircle? Similarly for edges on the incircle? Similarly for polyhedra?

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Mobile Email from a Cingular Wireless Customer http://www.cingular.com

Misère hex

The grave accent goes on the second e. Search misere hex without the accent. I'd like to see a computer program that plays (aka) "Rex" well.

Math fonts

By dropping the fonts from the symfont fix package into ~/.fonts, one can view pages like Mathematical Constants and Computation, Perimeter of an Ellipse, and pages converted by T_TH. I still don't fully understand why the font gets recognized as iso8859-1, even though the EncodingScheme is ``FontSpecific''. One also needs to use a ``recent'' (probably GTK2+) build of Firefox or Mozilla, the kind that try to do antialiased fonts. It might be necessary to run fc-cache to generate the index files.

jsMath displays some awesomely rendered mathematics. drop the BaKoMa Tex fonts into ~/.fonts. The fonts are supposedly also available at CTAN and mozilla mathML

inch centimeter 127

In the olden days, the centimeter was defined in terms of the inch: 10000/3937, but now the inch is defined in terms of the centimeter: 254/100. It's interesting how 127 divides both 3937 and 254.

Firefox extensions

Tried a bunch of Firefox extensions. FlashGot's build gallery feature is cool, once I figured out how to get it to work. It would be nice if it could work on all links on the page. It gets confused by HTML entities, e.g., %20 for space. Thumbs is nice in the unusual case that every linked HTML page has a picture on it. Down Them All was usable. All-in-one gestures is nice when I remember to use the gestures. Clusty works correctly in the canonical example of "saturn" (but is useful as a website). Linky is cool, as is GoogleBar's "reverse link" search. Coralize this link extension is great.

How to memorize 81 bits

Color each grid square by the bit, and remember the shape of the bits, and the letters they correspond to.

yo car caul
ga pet dron
ex sho ambi
ot wer dext
ic ing rous
an con
ti fig  e  van
bo ura  du  it
dy ble  cat  y
        ions

Scroll-wheel app-switcher

Scroll the mouse-wheel on the desktop to switch (and cycle) between windows of running applications. (No window manager I know does this by default, yet.)

Factoring Ramanujan's Constant

exp(pi*sqrt(163)) = 262537412640768744 ( 2 2 2 3 10939058860032031 (2 3 5 7 13 179 (2 88 (2 2 2 11)) 6959 (2 7 7 71) 3216751 (2 3 5 5 5 4289 (2 2 2 2 2 2 67))))

Unsolved instance of the Post Correspondance Problem

{(10,0),(0,001),(001,1)} Ling Zhao's PCP page

Prove it has no solution...
Also given in bit-flipped form as (6.15) in his Master's thesis: {(110,1), (1,01), (0, 110)}

1- in Lisp is pred in Haskell

The handy function 1- in Lisp is pred in Haskell, also (subtract 1) and (-1) by operator lambdas.

RFC 2409, RFC 3526, and "bad" generators

The two RFCs specify 2 as a generator for the prime Diffie-Hellman fields. However, 2 is not a generator: for example:

RFC 2409 - The Internet Key Exchange (IKE)

6.1 First Oakley Default Group

FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF

? p=2^768-2^704-1+2^64*(floor(2^638*pi)+149686)
%41 = 1552518092300708935130918131258481755631334049434514313202351194902966239949102107258669453876591642442910007680288864229150803718918046342632727613031282983744380820890196288509170691316593175367469551763119843371637221007210577919
? isprime(p)
%42 = 1
? j=2;
? (p-1)%j
%44 = 0
? q=(p-1)/j;
? isprime(q)
%46 = 1
? Mod(2,p)^q
%47 = Mod(1, 1552518092300708935130918131258481755631334049434514313202351194902966239949102107258669453876591642442910007680288864229150803718918046342632727613031282983744380820890196288509170691316593175367469551763119843371637221007210577919)
? znprimroot(p)
%48 = Mod(7, 1552518092300708935130918131258481755631334049434514313202351194902966239949102107258669453876591642442910007680288864229150803718918046342632727613031282983744380820890196288509170691316593175367469551763119843371637221007210577919)

The reason is buried Appendix E of RFC 2412 (uncited): " Using 2 as a generator is efficient for some modular exponentiation algorithms. [Note that 2 is technically not a generator in the number theory sense, because it omits half of the possible residues mod P. From a cryptographic viewpoint, this is a virtue.]"

One wonders why they didn't use a multiplier (instead of 149686) for which 2 really is a number-theoretic generator.

Unfriendly primes

Reply from On-Line Encyclopedia

./x.primes-2.ll.x primes 10000 | drop.pl 4 | xargs -n1 -i expr '{}' - 1 | xargs -n1 factor | perl -nlwe 'BEGIN{$f{2}=0}($a,$b)=/(.*):.* (\d+)/;$a++;$f{$a}=$f{$b}+1;END{print "$f{$_} $_" for(keys %f)}' | sort +0n +1n | perl -nwae 'BEGIN{$p="-1"}print if $p!=$F[0];$p=$F[0]'

Better is
./x.primes-2.ll.x primes 2000000 | drop.pl 4 | xargs -i expr '{}' - 1 | xargs factor | perl -nlwae 'BEGIN{$f{2}=0}($a=$F[0])=~s/://;shift@F;$m=0;for(@F){if($f{$_}>$m){$m=$f{$_}}}$f{++$a}=$m+1;END{print "$f{$_} $_" for(keys %f)}' | sort +0n +1n | perl -nwae 'BEGIN{$p="-1"}print if $p!=$F[0];$p=$F[0]'
First difference is at 239 (238: 2 7 17).

./x.primes-2.ll.x primes 2000000000 | drop.pl 4 | xargs -i expr '{}' - 1 | xargs factor | perl -nlwae 'BEGIN{$f{2}=0;$x=0} ($a=shift@F)=~s/://;$m=0; for(@F){if($f{$_}>$m){$m=$f{$_}}} $f{++$a}=++$m;if ($m>$x){print $a;$x=$m}'

Memorizing 81 bits

Y O G A	C A R P E T	C A U L D R O N
E X O T I C	S H O W E R I N G	A M B I D E X T R O U S
A N T I B O D Y	C O N F I G U R A B L E	E D U C A T I O N S	V A N I T Y

Y O G A	C A R P E T	C A U L D R O N
E X O T I C	S H O W E R I N G	A M B I D E X T R O U S
A N T I B O D Y	C O N F I G U R A B L E	E D U C A T I O N S	V A N I T Y

Mersenne 42 in other bases

The 42nd known Mersenne prime 2^25964951-1 was discovered recently. The minus-one factorization of the exponent is 25964951 (5 5 11 17 2777 (2 2 2 347 (2 173 (2 2 43 (2 3 7))))).

2^25964951-1 in base 94

2^25964951-1 in base 52

The huge pages of ``random'' characters inspire the Word-search Problem: given a string S, and a target word T (or a list of target words), find T= S[a]S[b]S[c]... where the indices a,b,c... are in arithmetic progression.

IRC is an Internet Push Technology

One must query a RSS feed continuously to get real-time updates, which will usually get you banned (try the Coral distribution instead). Is there a better "push" solution?

Yes. IRC.

NIC GPS

What if all network cards had GPS receivers? They would provide the link between the physical and cyber worlds.

--

Mobile Email from a Cingular Wireless Customer http://www.cingular.com