The Starburst Challenge

[modest]

yep. I get,

 

1285358318908397602470209924419

1661560552392525585160103959383

6999877434399668574208978696257

9490563061063114787872069073122

3654243263896217757461280490461

5383923706203251445980569041004

3909675534270085037917881294453

9164698176655126622658593734103

4427727108327034298466549595194

2329084741660338602493311358287

5853230435601156862113013919136

1292134582394979068247990236647

5309148602877694603617973626389

1418151225133359596237633826198

98720804485492408275604248046875

 

what does it say?

 

~modest

[Donk]

It doesn't say anything yet. It's just one of the building blocks that I'm hoping to use to construct the number. Watch this space...

[CraigD]

Are there any mad mathematicians around who can confirm that 296,395^85 multiplies out to the above? My calculator won't go that high <grin>

If you don’t have an arbitrary precision calculator local to you computer, there are some online ones, the awesomely versatile, local clipboard friendly, and easy-to-make an URL WolframAlpha website, for example: http://www.wolframalpha.com/input/?i=296395^85.

 

A WolframAlpha tip – be sure to click “more digits”, then rightclick on the result to display copyable plaintext. Unfortunately, you can’t select all on just a single result pane, so must highlight the whole result to copy it.

 

For intense number crunching, you’ll likely want one you can program with – nearly all programming languages have either intrinsic or library-based arbitrary precision calculators.

 

Enjoy! :)

[freeztar]

I've explored this problem many, many years ago. Kudos Donk for resurrecting this thread!

 

I like the idea of fractals, but it seems limited for this purpose. (unless they are layered in some cohesive manner?)

 

It seems dimensions need to play. Perhaps a recursive directory-type structure would suit? Nah...

 

It would have to be a new idea, like when time was added to the mathematical lexicon. A perceptual shift more than a revolution of theory....

 

Good stuff...

[CraigD]

After a long pause and a nudge from me, some new attention on this old challenge from the “Need A Project” thread:

[The Starburst Challenge] looks fairly simple to solve to me. let's make our alphabet 27 characters, A-Z and space.

then simple make the compression alphabet 27^2 = 729 characters. we can use Chinese characters or something, what we use doesn't matter too much, as long as we know what number it represents. then conversion from our Chinese alphabet to our English one is 2-1, making it very straight forward.

I don’t understand how this approach could be used to solve the challenge, but if it makes sense to you, go ahead and try using it.

 

Note that your goal is to write an arithmetic expression that evaluates to an number that can be converted to a readable English language text. Here’s an incorrect example:

The 13-character expression

38!*2/3+12^40

evaluates to

363379460657424939012499038283533286926974976

. If it has instead evaluated to

364320551715098739100288990406051850229694140

, which written in base 32, with space=0, A=1, ….Z=26, “.”=27, “?”=28 is the 30-character string

“HELLO HYPOGRAPHY. HOW ARE YOU?”

, I would have considered it to have weakly satisfied the challenge, because 13 characters could reasonably be considered “much less” than 30 characters.

 

38!*2/3+12^40 misses the target number slightly, by a mere 0.26%, but even this small a mismatch using a fixed base encoding/decoding scheme results in a near complete loss of the desired message - 38!*2/3+12^40 in base 32, as above with added character mapping “,”=29, ”-“=30, “’”=31 is

“HDVYBBAVEKIAYSZKTXCH'-Z” followed by 7 spaces.

[phillip1882]

so i wanted to come back to this because i was studying lossless compression.

part of the problem of the starburst challenge is that its very difficult to express large numbers with a high degree of accuracy. for example, simply multiplying several large numbers may give you a very accurate result, but you would need roughly as many digits as the number itself. this means you either need powers or factorials to reduce. powers are the easiest to manage so lets try that. heres a poem i wrote about go a while back, lets see if we can conquer that.

i have come into being, placed by the hand above into the great unknown,
separated from my collective, from the basket of true like-minded stone.
seeing my new surroundings, a thick wooden board with a celestial grid,
it does not bode well, I am unable to breathe with the congestion it bids.
a sacrificial piece then, an example to others not to follow alone,
my new fate I cannot control, beyond which lies my enemy's captive home.
more of my allies are placed nearby, they are to live, for nowhere else to try.
sleep soon fills and consumes me, because my position has become unsettled,
yet it is not all for not, my master has won and he bids me home again.

so, space will be 0, a-z 1-26 , "," 27, and "." 28,  giving us base 29.

then in decimal we have the number...

54524821107009630686811953676000240682770879909027006382907941107712991285409808
14547711317969397206749105005495393811107613069004096592771598848094484916907869
93146380072751235488078863131667654022512635615271163584552116329792199943947088
58216500110606575412728970299912316579919135232731910251995996207991779324836120
00964297318907382941755396037604576711024470474005544398909976864684527291401757
67983103737735165499186777006462834408325709547578945872275885124866797119437627
82623685928319329666000698240963268040755052733580456487834251619902608086974935
97691296349745069729297086901424767510938032643119758776628155708101255772444286
58799476856347758431863273335493587508517196821067226844514962772384006386893247
41486253801457541045126713131789917422537906706522046038439701873228175899878570
97923324857198442092995205355556582927817484004410770018923644789632448693956832
02850846380220811625732840383747801389730164725760259350810518154484407209734649

91662040236924386800547234951775312680509034487003148040427720000358803722703656
1302071

 

the most i can compress it using the same power  base is the following...

 

131966*17249876309^94+1049607975*17249876309^93+2980840835*17249876309^92+

1298916032*17249876309^91+9764091693*17249876309^90+1702920020*17249876309^89+

4789097238*17249876309^88+9377139493*17249876309^87+8936694759*17249876309^86+

10810571207*17249876309^85+6841395336*17249876309^84+11415554916*17249876309^83+

3056323121*17249876309^82+284329932*17249876309^81+7243053432*17249876309^80+

16064925347*17249876309^79+12064093747*17249876309^78+6659770685*17249876309^77+

12280642305*17249876309^76+6609865981*17249876309^75+3056641861*17249876309^74+

3548896527*17249876309^73+8471442633*17249876309^72+3446354624*17249876309^71+

9363091416*17249876309^70+11855469099*17249876309^69+5422743220*17249876309^68+

2491753081*17249876309^67+10789433478*17249876309^66+20588874*17249876309^65+

11718266096*17249876309^64+10894908027*17249876309^63+92791749*17249876309^62+

9332634309*17249876309^61+475596374*17249876309^60+3569964887*17249876309^59+

644455531*17249876309^58+53876730*17249876309^57+2990620621*17249876309^56+

12064094989*17249876309^55+4280253129*17249876309^54+198747908*17249876309^53+

11875980212*17249876309^52+2160190173*17249876309^51+841355050*17249876309^50+

2988461975*17249876309^49+30417985*17249876309^48+8069491469*17249876309^47+

322012713*17249876309^46+298253676*17249876309^45+133979327*17249876309^44+

29376302*17249876309^43+284338904*17249876309^42+124266137*17249876309^41+

62594403*17249876309^40+72501465*17249876309^39+7691734598*17249876309^38+

8410139029*17249876309^37+4767298197*17249876309^36+8245615775*17249876309^35+

13714888439*17249876309^34+12096749135*17249876309^33+7855074172*17249876309^32+

2984872556*17249876309^31+29298922*17249876309^30+33364628*17249876309^29+

659991140*17249876309^28+966071017*17249876309^27+4878825706*17249876309^26+

420842570*17249876309^25+3528077099*17249876309^24+8651661036*17249876309^23+

111510733*17249876309^22+8936956274*17249876309^21+11551448712*17249876309^20+

9239924303*17249876309^19+7527627962*17249876309^18+2102520566*17249876309^17+

11310982406*17249876309^16+3036885626*17249876309^15+8245885297*17249876309^14+

12092017655*17249876309^13+11303182577*17249876309^12+2989327096*17249876309^11+

12146256901*17249876309^10+3384575915*17249876309^9+11311927689*17249876309^8+

7384173111*17249876309^7+8649998254*17249876309^6+267832592*17249876309^5+165260546*17249876309^4+

8328578593*17249876309^3+2975754583*17249876309^2+7835467027*17249876309+25494508

 

and strict descending factorial produces a worse result.

however if i simply state, let x = 17249876309,

31966*x^94+1049607975*x^93+2980840835*x^92+1298916032*x^91+9764091693*x^90

+1702920020*x^89+4789097238*x^88+9377139493*x^87+8936694759*x^86+10810571207*x^85

+6841395336*x^84+11415554916*x^83+3056323121*x^82+284329932*x^81+7243053432*x^80

+16064925347*x^79+12064093747*x^78+6659770685*x^77+12280642305*x^76+6609865981*x^75

+3056641861*x^74+3548896527*x^73+8471442633*x^72+3446354624*x^71+9363091416*x^70

+11855469099*x^69+5422743220*x^68+2491753081*x^67+10789433478*x^66+20588874*x^65

+11718266096*x^64+10894908027*x^63+92791749*x^62+9332634309*x^61+475596374*x^60

+3569964887*x^59+644455531*x^58+53876730*x^57+2990620621*x^56+12064094989*x^55

+4280253129*x^54+198747908*x^53+11875980212*x^52+2160190173*x^51+841355050*x^50

+2988461975*x^49+30417985*x^48+8069491469*x^47+322012713*x^46+298253676*x^45

+133979327*x^44+29376302*x^43+284338904*x^42+124266137*x^41+62594403*x^40+72501465*x^39

+7691734598*x^38+8410139029*x^37+4767298197*x^36+8245615775*x^35+13714888439*x^34

+12096749135*x^33+7855074172*x^32+2984872556*x^31+29298922*x^30+33364628*x^29+659991140*x^28

+966071017*x^27+4878825706*x^26+420842570*x^25+3528077099*x^24+8651661036*x^23+111510733*x^22

+8936956274*x^21+11551448712*x^20+9239924303*x^19+7527627962*x^18+2102520566*x^17+11310982406*x^16

+3036885626*x^15+8245885297*x^14+12092017655*x^13+11303182577*x^12+2989327096*x^11

+12146256901*x^10+3384575915*x^9+11311927689*x^8+7384173111*x^7+8649998254*x^6+267832592*x^5

+165260546*x^4+8328578593*x^3+2975754583*x^2+7835467027*x+25494508

1481 characters, compared to 1059 characters in the original data. while this is obviously not compression, it suggests that for very large documents this type of compression is possible.

Edited January 10, 2018 by phillip1882