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 what to do with the data? 
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Posted on: Thu Mar 01, 2012 5:59 am




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Post Re: what to do with the data?
All this is very interesting. And starling, I did read through your entire post and found more than one interesting point. (Aside: You go to church? What denomination/faith are you? Just curious because you sound like a regular and I go to church too.)

Like picklepep, I have some similar memories as well... Math Team sort of stuff although here in Canada maybe it doesn't work quite the same way. Also Waterloo Math Competition, mensa stuff, etc. I liked doing math "puzzles" too from an early age, but I don't think I really got much into Sudoku, Kakuro, KenKen and the like until recent years. I probably started doing them because I need something math-related to keep my brain sharp. (I studied Mechanical Engineering but now I'm teaching music which is kind of a different thing!) Something else I do now to keep my brain sharp is speedcubing, but that's not directly number related.

Probably both things 1) having learned the math language at critical age and 2) current age both factor into how fast one can do timed puzzles. Perhaps I'm just a bit faster than picklepep because I'm 7 years younger (30). I think after the age of 22 you don't regenerate cells like you did before and anyway I've lost too many brain cells over my kids. [razz] (Just had to blame the kids hehe.)

As for browser type, I'm on Firefox.


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Posted on: Thu Mar 01, 2012 7:33 am




Posts: 175
Joined: Fri May 13, 2011 2:11 am
Post Re: what to do with the data?
sneaklyfox wrote:
(Aside: You go to church? What denomination/faith are you? Just curious because you sound like a regular and I go to church too.)

Baptist, though that's more a byproduct of living in the South than actual doctrine. I'd probably be most accurately classified as a Reformed Baptist, though that's not perfectly accurate either.

I actually totally agree with both of you that among speakers of the language, age helps heavily to delineate.
That is, being 18 probably does give me some level of advantage over you two.

picklepep wrote:
Yet I still fall far far behind both you sheldolina.


I feel like on a day to day basis, your best time is pretty consistently within 1-2 seconds of what I expect to do on an average puzzle. You're not very far behind at least me at all.

As for your best time, which is the category you're furthest behind us on, that really does have a lot to do with getting the right puzzle. The 6 4x4's I've done in the 4-5.5 second range all were puzzles that, because I speak the language, immediately to me interpreted as a complete sentence, and so there was no thought on which number went where, just thought on typing everything as fast as possible. For you, what likely happens is that you see the puzzle and the sentence, but can't enter it fast enough.

In other words, I expect that at the upper levels of rankings, best time is where age/typing speed impacts more heavily than anything else, since it's among a bunch of fluent people (A complete sentence in Cantonese is going to sound like nothing meaningful to me, so I couldn't know if it's a complete sentence or not, but a bunch of native English speakers hearing English phrase after phrase will eventually notice a complete sentence among them, and all it takes is one.), whereas average time is more impacted by speaking the language or not (That is, a native English speaker will be able to piece together more sentence fragments into a cohesive thought than a non-native one.)

But yeah, in the small sample size, you're right that age does appear to help several people quite thoroughly.

Actually, now that I think about it, the biggest example of the gap in the top end of timed and the middle was a day when the top 13 4x4 times at the end of the day were all from either Sheldolina, Sneaklyfox, Patrick, picklepep, or me, which as we've found now, is people of ages 13, 30, (I'm not sure, but I don't think he's even 35, and that was the highest possible endpoint for his age in my head), 37, and 18, which is younger than a lot of the other solvers have stated their age to be (The last discussion of this included a few people above 60, and not many people under 40 other than those already noted.).

Further, we know now that at least 4 of those people are definitely people who learned how to puzzle in their critical period (Well, I'm still assuming sheldolina isn't beating me on the first puzzles she's ever done and had learned how to puzzle a little earlier than, say, yesterday), and the other is Patrick, so presumably he did too. What that means, then, is that those are people who simultaneously have age and language on their side, which may indeed be what has to be had in order to excel at timed puzzles.

As for speedcubing, I've never actually learned how to. The algorithms just have never been an interest of mine. My roommate loves the larger cubes, though.


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Posted on: Thu Mar 01, 2012 11:14 am




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Post Re: what to do with the data?
pharosian wrote:
I've just read your paper on "Choice of Browser and Numerical Intelligence," and I think your conclusion that Chrome users have the highest numerical intelligence is based on incomplete data. That is, you only had the raw times and browser type on which to base your conclusion.

Yes, that was the data that was available and used, no less, no more..
pharosian wrote:
But given that you found no statistical difference between browser types for the non-timed puzzle

That is saying something completely different, namely that people tend to solve the same "amount" of regular puzzles.
You can't really connect performance (/intelligence) to that other than if maybe one group of people got points mostly by
doing lots of easy puzzles, and others by doing a few hard puzzles.
pharosian wrote:
and the statement made elsewhere on this forum that younger solvers do better on the timed puzzles,

I can't base anything on a statement made by someone on the forum..
pharosian wrote:
I think if you had access to the age of each solver you would find that a more appropriate conclusion is that "Chrome users are typically younger than IE (and Firefox) users."
The older a person is, the more likely they are to stick with what they know and are comfortable with. Older people are (on average) also less technically inclined than the new generation that can't remember a time before they had access to a personal computer and the Internet.

Yes, this fits with the "We can only speculate ..." bit in the conclusion: I can't claim anything based on information I don't have.
It's fine to speculate of course (so yes, it may be true that Chrome users are younger on average, and that younger people
have faster brains, so they're better at doing these puzzles, but again, that's only speculation)
pharosian wrote:
Pharosian -- whose primary browser is Safari

Safari users did quite well, if I remember correctly. I should look into what is the minimum sample
size for reporting a meaningful result, maybe I can include Safari :-)

Patrick


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Posted on: Thu Mar 01, 2012 3:50 pm




Posts: 690
Joined: Fri May 13, 2011 6:51 pm
Post Re: what to do with the data?
pnm wrote:
pnm wrote:
So now the milestone of 1 million solved puzzles has been reached,
what to do with the data?

Alright, as you saw on the main page, I've done something with the usage data... :-)

This took a _long_ time to produce (most of my spare time in the past two months),
I'll be happy to go back to programming on the site again.. [mellow]

Patrick


As usually you initiate a nice debate on some subjects. It’s a very interesting work that correlates the “performance” of the calcudokers versus the type of browser; I am sure that with a wider sample (specially in timed puzzles) you would get additional interesting results, let’s wait to the 2 million solved puzzles). However (and a little in the line of the pharosian’s comment) I think that it is difficult to extrapolate many conclusions in the field of the “numerical intelligence” itself (I will comment on this at the end); if we had an “age curve” or age histogram (this is not possible since even considering that you ask for the age at the moment of signing in the page, the information would not be absolutely confident) we could see perhaps that younger puzzlers use more the Chrome, for instance, but that’s not the target of this study, etc... and it's only a speculation at this moment.

I will comment first on the “solving rate”. I am a little confused. When you say (page 2):

“Figure 1 shows an example simple 4 x 4 puzzle and its
solution. Figure 2 shows a much harder 6 x 6 puzzle. The
difficulty of a puzzle is estimated by averaging the natural
logarithm of the number of possible permutations for each
row and each column (after applying the restrictions im-
posed by each cage), divided by the size of the puzzle (for
example, the puzzle in Figure 1 has a rating of 0, the puzzle
in Figure 2 a rating of 62).”


As you know the total number of valid 9x9 sudoku grids (Felgenhauer & Jarvis) is 6,671 x (10 ^ 21). This is the full “Universe” of "sudoku grids" (9x9’s), with the sudoku restrictions, obviously if we impose restrictions (cages), eliminating the sudoku restriction (1 to 9 in every 3x3 box) this number would probably decrease dramatically. But even considering that terrible number, 6670903752021072936960, the natural logarithm is 50.252 … and dividing by 9 gives 5.5836, so this would be the maximum solver rating for any 9x9 calcudoku. In a practical case, with the restrictions (cages) there, assuming, let’s say, 1,000,000,000 of permutations, the natural log is 20.723 … and divided by the size 9 gives 2.3026 as the “solving rate”. So something must be wrong in that expression, perhaps is “multiplied by …”, etc. (in the past when we have discussed about the “solving rate” we probably entered in the field of the “trademark” or “owner's information” (in this case, Patrick, I would understand that you do not give more details). And how to calculate all the "free permutations"?.

Previously, I was thinking that you were using other parameters to “measure” the “solving” rate”, as the time elapsed by the computer in finding the solution, the size of the cages, the number of individual cells initially given, etc...

With respect to the “numerical intelligence”: I am not very sure about the extended use of this concept, most numerical IQ tests include not only the four basic arithmetic operations but, additionally, problems with series, operations with square roots, operations with fractions, numerical structures, etc., what I mean is that only the operations of the timed puzzles (for instance) are not enough to conclude about “numerical intelligence” in an "academic" sense (and also one important parameter for most “numerical IQ tests” is the age once again); inversely, let’s think in what most people would define as a “genius”, with a “really high numerical IQ”, a person able to quickly multiply 2 numbers of 10 digits each, for instance, would that person be the faster one solving the timed 4x4’s, 5x5’s and 6x6’s?); some correlation exists, undoubtedly, but we must be a little careful (though the abstraction capacity, numerical memory, etc., have important influence in the case of timed puzzles, and, possibly, having good practice with keyboards, joysticks, etc.). In the case of the regular puzzles, and considering the actual special operations involved (negative numbers, bitwise OR, mod, exponentiation, etc…), some previous degree of knowledge in mathematics is necesssary and we would need to estimate the fact that not having that previous knowledge does not imply lower numerical IQ.

P.D.: An additional calculation on the "solver rating".
The total number of permutations of a row, i.e., is 9! so, even without any limitations (the additional condition for the different numbers by column), if we consider all combinations 9! x 9! x ... (nine times in total) ... x 9! and we take the natural logarithms we have ln(9!) + ... (nine times in total) ... + ln(9!) = 9 x ln(9!), if now we divide by 9 (the size of the puzzle) we obtain ln(9!) = 12,80 which is much lower than the usual ratings or the calcudokus 9x9.


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Posted on: Thu Mar 01, 2012 6:02 pm




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Location: Canada
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Post Re: what to do with the data?
starling wrote:
Baptist, though that's more a byproduct of living in the South than actual doctrine. I'd probably be most accurately classified as a Reformed Baptist, though that's not perfectly accurate either.


Ok, I see. That's neat. Our church is Alliance (C&MA... Christian & Missionary Alliance).

starling wrote:
As for your best time, which is the category you're furthest behind us on, that really does have a lot to do with getting the right puzzle. The 6 4x4's I've done in the 4-5.5 second range all were puzzles that, because I speak the language, immediately to me interpreted as a complete sentence, and so there was no thought on which number went where, just thought on typing everything as fast as possible. For you, what likely happens is that you see the puzzle and the sentence, but can't enter it fast enough.


Both getting the right puzzle and being in the right frame of mind. As noted somewhere else in the forum, some days are better than others. Less tired, etc. Speaking of which, I notice that recently I've been doing worse in the timed puzzles, more noticeably in the 4x4s and I realized yesterday that I had better reboot my computer because it would freeze for moments at a time and break the flow of the solve. I should have done it before I did the timed puzzles.

starling wrote:
As for speedcubing, I've never actually learned how to. The algorithms just have never been an interest of mine. My roommate loves the larger cubes, though.


I learned beginner's method back in the 80's and only learned the speedcubing methods in recent months but I'm totally into it now. I guess moving my hands and fingers at high speed is enjoyable too. Not a big fan of larger cubes in terms of doing it for speed... at least, I think having time to play with the 3x3x3 is enough for me right now. Still would like to get my hands on a 4x4x4 though...


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Posted on: Thu Mar 01, 2012 9:55 pm




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Joined: Mon Jul 25, 2011 7:49 pm
Post Re: what to do with the data?
Hi Patrick -

I just loved what you did with the data:
== I'm a chrome user, so you flattered me
== Your paper might be considered to gently ridicule those who write academic papers, which amused me
== You confirmed that you live in London, so you gave me pleasure in us both living in England.

Horray! Bravo!

(hey, people, calm down, this is intended to be light hearted)


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Posted on: Thu Mar 01, 2012 10:07 pm




Posts: 175
Joined: Fri May 13, 2011 2:11 am
Post Re: what to do with the data?
sneaklyfox wrote:
starling wrote:
Baptist, though that's more a byproduct of living in the South than actual doctrine. I'd probably be most accurately classified as a Reformed Baptist, though that's not perfectly accurate either.


Ok, I see. That's neat. Our church is Alliance (C&MA... Christian & Missionary Alliance).

I'm not going to lie, I had to cheat and wikipedia what the C&MA was... Apparently there are tons of C&MA churches in Birmingham, but Birmingham is so full of mega-churches that some smaller churches don't get their name out there.

From wikipedia's list of the general beliefs of C&MA churches, I agree with everything, though part of that likely results from how dogmatic a lot of the stuff there is. The one doctrinal issue, the eschatological stuff, I do agree with, though.

As for the rest of the thread:

I've talked to Patrick about trying to get together some form of a survey of age, gender, education, and how long you've been doing puzzles linked to account and browser for the sake of having some data to prove the age oriented hypothesis.

Honestly, right now, we don't have enough data to prove half the hypotheses that we're assuming; My language thing is dependent on that last one, the common age-skewing-the-data hypothesis is dependent on the first. We have anecdotal evidence to support some of these, but as the phrase goes, anecdote is not the singular of data.

clm, on the solver rating, I was assuming there was some factor it was multiplied by so that you didn't just end up with a bunch of meaninglessly close decimals.


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Posted on: Thu Mar 01, 2012 11:05 pm




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Post Re: what to do with the data?
starling wrote:
I'm not going to lie, I had to cheat and wikipedia what the C&MA was... Apparently there are tons of C&MA churches in Birmingham, but Birmingham is so full of mega-churches that some smaller churches don't get their name out there.

From wikipedia's list of the general beliefs of C&MA churches, I agree with everything, though part of that likely results from how dogmatic a lot of the stuff there is. The one doctrinal issue, the eschatological stuff, I do agree with, though.


Well I cheated and checked what Reformed Baptist was too although I know a little about Baptist. I'm no Calvinist though. More Arminianist, but not exactly... depends which type maybe. And I also cheated and had to look up "eschatology" on dictionary.com. Speak about math language, you're probably better in English than I am!

starling wrote:
I've talked to Patrick about trying to get together some form of a survey of age, gender, education, and how long you've been doing puzzles linked to account and browser for the sake of having some data to prove the age oriented hypothesis.


I always thought that would be pretty neat too. If this ever happens, I would be all for it!


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Posted on: Fri Mar 02, 2012 12:07 am




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Post Re: what to do with the data?
starling wrote:
clm, on the solver rating, I was assuming there was some factor it was multiplied by so that you didn't just end up with a bunch of meaninglessly close decimals.

True, I may have forgotten to mention a factor of 10 in there, I'll double-check.

Patrick


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Posted on: Fri Mar 02, 2012 6:18 am




Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Post Re: what to do with the data?
Patrick, concerning the calculation of difficulty of a puzzle, as quoted by clm from your paper, you say:

Quote:
“The difficulty of a puzzle is estimated by averaging the natural logarithm of the number of possible permutations for each row and each column (after applying the restrictions imposed by each cage), divided by the size of the puzzle (for example, the puzzle in Figure 1 has a rating of 0, the puzzle in Figure 2 a rating of 62).”


I would like to use the same method to estimate the difficulty of my puzzles, but I am not sure about how you apply the cage restrictions. This is what I think you might be doing, using as an example the top row of today's 9x9 puzzle (2 cells of a 4-cell 288x, 2 cells of a 4-cell 0-, a 1-cell 1, a 2-cell 8+, and a 2-cell 54x):

288x is obtained by multiplying the prime factors 2222233. The resulting combinations are 9841, 9822, 9442, 8661, 8632, 8433, and 6642. This means that the 2 cells in the top row can contain one of the following 17 combinations: 98, 94, 92, 91, 86, 84, 83, 82, 81, 64, 63, 62, 61, 43, 42, 41, and 32, which generate 17 x 2 = 34 permutations.

0- can be obtained with the following combinations: 9711, 9621, 9531, 9522, 9441, 9432, 8611, 8521, 8431, 8422, 8332, 7511, 7421, 7331, 7322, 6411, 6321, 5311, 5221, and 4211. As a result, the 2 cells in the top row can contain one of the following 31 combinations: 97, 96, 95, 94, 93, 92, 91, 86, 85, 84, 83, 82, 81, 75, 74, 73, 72, 71, 64, 63, 62, 61, 53, 52, 51, 43, 42, 41, 32, 31, and 21, which generate 31 x 2 = 62 permutations.

8+ can be obtained with the 3 combinations: 71, 62, and 53, which generate 3 x 2 = 6 permutations.

Finally, 54x can only be obtained with the 2 permutations 96 and 69.

In total, the number of possible permutations for the top row without considering repetitions but taking into account the cage restrictions is: 34 x 62 x 1 x 6 x 2 = 25296, and log(25296) = 10.1384.

Then, if I do the same with the other 8 rows and for the 9 columns, add up the 18 logarithms and divide the result by 162, I obtain the estimated difficulty.

Is it how you do it?


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