Decoding the Art Critic's Letter: Uncovering His Favorite Works of Art

[tribdog]

I once knew an art critic who was also a brilliant mathematican, unfortunately he couldn't read. He could understand letters as variables and oddly enough acronyms, but not as words. So when I received a letter from him telling me which three works of art are his absolute favorites of all time it took me a couple of minutes to decipher his math into my language. Here's what his letter said:
1.)(8,2,5): 55,65,150,175,185,210,295,305

2.)(8,4): 6:55, 4:02, N:30 (8<n<3)

3.)(1,1,6): CCW:a>b>c>d>e>a>b>c>d>e...

Can you figure out the three works of art and who the artists were?

 

[gauravkukreja]

WHich is greater?
31^11 or 17^14

 

[Galileo]

31^11 = 25408476896404831
17^14 = 168377826559400929

So 17^14 is biggah

 

[shmoe]

without a calculator or computer, notice that (in white):


31^11<(2^5)^11<2^55<2^56<(2^4)^14<17^14

 

[tribdog]

no attempts even? okay here is a clue the numbers inside the parenthesis refer to the number of letters in the artists name. The names of the paintings are not spelled out in any way by the code.


More of a clue follows a few lines down.



the number of letters in the artists name in painting 1 could also be written as (8,7)
the clues to painting number 2 refer to time
the clues to painting number 3 refer to elevation. > is greater than

 

[Gokul43201]

I think I know the first painter, from your above extra clue...guessing the painting will need some time.

<select> Da Vinci...don't know painting yet [/color]

I think #2 is Dali, Persistence of Memory[/color]

#3 . Could this be Escher, either the one with the stairs or the one with the waterfalls (or some other painting along this theme) ?[/color]

 

[Gokul43201]

Thinking aloud :

#1 has 8 numbers, all multiples of 5..signifying what...I don't know. But might it be useful to note that there are 8 different things involved in the painting ?

It can't be MONA LISA ... which has 8 letters, but according to your hint, that can't be it.
The dominant number in the Last Supper would be 12 or 13. (Aside : I previously thought #2 might be the Last Supper, because John 6:55 says " For my flesh is true food, and my blood is true drink")
The few other paintings I know are the Vitruvian (sp?) Man, Madonna of the Rocks, and the Magi painting. [/color]I'm leaning towards the first of these, but nothing concrete yet.

 

[tribdog]

You are a smart smart PFer.

 

[Gokul43201]

<select> It is the Vitruvian Man...these are roughly the angles made by hands and legs. Obvious once you see than N(i) + N(9-i) = 360, for i = 1,2,3,4[/color]

 

[DivineNathicana]

Wow, that's a brain killer. But I'm figuring that #1 is da Vinci and #2 Dali. That's as far as I got = ) heh.

- Alisa

 

[Noticibly F.A.T]

hey shmoe i don't get it

 

[TenaliRaman]

another brilliant work of shmoe there,
(check between :: and ::)
::
31 < 32 ... (Order of Natural Numbers -- Peano's Axiom)
31 < 2^5 ... (since 2^5 = 32)
31^11 < (2^5)^11 ... (Raising both sides to power of 11)
31^11 < 2^55 ... (Laws of indices) .. *

But,
2^55 < 2^56 ... (Laws of indices) .. **

therefore from * and **,
31^11 < 2^56 ... (Transitivity)
31^11 < 2^(14*4) ... (bcos 14*4 = 56)
31^11 < (2^4)^14 ... (Laws of indices)
31^11 < 16^14 ... (2^4 = 16) .. ***

But,
16 < 17 (Order of Natural Numbers -- Peano's Axioms)
16^14 < 17^14 ... (Raising both sides to the same power of 14) .. ****

therefore from *** and **** we get,
31^11 < 17^14 .. (Transitivity)
[/Color]::

-- AI

 

[Gokul43201]

That is quite nice.

I did it the clumsy way...albeit using only paper and pencil...and got lucky !

Compare 11*log31 and 14*log17

This takes a lot longer to write down here than to actually do...

log 30 = 1 + log3 = 1.477 and log 33.3 ~ 2 - log3 = 1.523. A rough linear interpolation tells me that log31 ~ 1.49. So, 11*log31 ~ 16.4

log17 ~ log (100/6) = 2 - log3 - log2 = 2 - 0.778 ~ 1.22, so 14*1.22 > 14*1.2 = 16.8, which is the bigger of the two.

PS : It helped that I know the logarithms of 1, 2, 3, 5, and 7...you can get most others pretty quickly from these.

 

[Noticibly F.A.T]

Now i get it. Thanks tenaliraman