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92 have him in circles

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And Vietnamese style Pho﻿
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This is so unlike all the recordings I've heard of this Waltz... so refreshing!﻿
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Golden Gate, Sunset
Yesterday evening shot.  Now when we reviewed images I've got, I understand how lucky we are to catch such sunset spending only 6 days in SF.
More to come! BTW, this is three 2Ev bracketed shots in one.. some people will call it HDR:-))﻿
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Euler 216: Primality of number of the form: 2*n^2 - 1.

Consider numbers t(n) of the form t(n) = 2n2-1 with n  1.
The first such numbers are 7, 17, 31, 49, 71, 97, 127 and 161.
It turns out that only 49 = 7*7 and 161 = 7*23 are not prime.
For n  10000 there are 2202 numbers t(n) that are prime.

How many numbers t(n) are prime for n  50,000,000 ?

-------------------------------------------------------------
Playing around with this expression a bit, I arrive at

2*n^2 - 1 = 2* (n-1) * (n+1) + 1
= 2* (n-i) (n+i) + (2*i^2 - 1)

Noted that the second term is the same as the original term,
just smaller.  This gives a hint on how to perform a quick sieve

Any better idea?﻿
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Could category theory help save privacy?

Jeremy Kun has a great blog article about encryption and privacy:

He quotes Obama as saying:

You can’t have 100% security and 100% privacy, and also zero inconvenience.

But he argues against this, pointing out:

There are two facts which are well known in theoretical computer science that the general public is not aware of. The first is about the privacy of databases:

There is a way to mine information from a database without the ability to inspect individual entries in the database.

This is known as differential privacy. The second is no less magical:

There are secure encryption schemes which allow one to run programs on encrypted data and produce encrypted results, without the ability to decrypt the data.

This is known as fully homomorphic encryption.

These ideas are exciting for lots of practical reasons.   The second one means that big companies and governments can do useful things with encrypted data you send them, and then send back the results for you to see, encoded in a way only you can decode... without them being able to know what your data was!

But as a mathematician, I really love how this is an example of category theory in action!

The funny diagram below expresses the key idea.  We start with a message m and encrypt it, getting the encrypted message enc(m).   This process is drawn as the vertical arrow at left, labelled enc.  Arrows are processes: things we can do.

Alternatively, we could run some program f on our message and get some output f(m) - that's what the horizontal arrow at bottom means.    Then we could encrypt that and get the encrypted output enc(f(m)).

But it would be really cool if anyone in the world could produce this encrypted output  starting with the encrypted message, but without knowing how to decode that encrypted message.

And they can.   There is a program, called eval in this picture, which takes enc(m) as input and produces the  encrypted output enc(f(m)).

So: going up the left-hand arrow and then across the top of the rectangle is the same as going across the bottom and then going up the right-hand arrow.  This is a very standard idea in category theory.

In short: eval(enc(m)) = enc(f(m)).

But the cool part is that anyone in the world can have access to the program eval but still not be able to decode your encrypted message.  So, people can do useful things with your data without ever knowing your data.  Privacy is preserved.

Thanks to for pointing this out.﻿
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7   53  183  439  863  497  383  563   79 {973} 287   63  343  169  583
627  343  773  959  943  767  473  103  699  303 {957} 703  583  639  913
447  283  463   29   23  487  463 {993} 119  883  327  493  423  159  743
217  623    3  399 {853} 407  103  983   89  463  290  516  212  462  350
{960} 376  682  962  300  780  486  502  912  800  250  346  172  812  350
870  456  192  162  593  473  915   45 {989} 873  823  965  425  329  803
973  965  905  919  133  673  665  235  509  613  673  815  165 {992} 326
322  148  972 {962} 286  255  941  541  265  323  925  281  601   95  973
445  721   11  525  473   65  511  164  138  672   18  428  154  448 {848}
414  456  310  312  798  104  566  520  302  248  694 {976} 430  392  198
184  829  373  181  631  101 {969} 613  840  740  778  458  284  760  390
821  461  843  513   17 {901} 711  993  293  157  274   94  192  156  574
34  124    4  878  450  476  712  914  838  669  875  299 {823} 329  699
815  559 {813} 459  522  788  168  586  966  232  308  833  251  631  107
813 {883} 451  509  615   77  281  613  459  205  380  274  302   35  805﻿
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Have him in circles
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My colleagues would really enjoy this video ... how to make pho ! :)﻿
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A new journey for me...﻿
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Times square on 9-11-2013﻿
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Great tips landscape photography.

Last Light on Half Dome
Physics was never one of my favorite classes as I took nearly two years of it in college, but I was fortunate upon graduating to get a job at the world's leading color printer manufacturer, where I was able to apply what I learned about the properties of light.  One of the interesting things about light and human color perception is that light which we perceive as having different colors can blend together to form other colors.  Blending primary colors red, green and blue results in colorless white light.  This property of light being "additive" and creating new colors has practical applications in landscape photography.

When you see an orange object, what color is it?  You perceive that the object is orange, but orange is actually the wavelength of the light reflected, so in a sense the object itself is every color but orange, orange is the light it doesn't absorb, the color of the light it rejects and sends towards us.  As a photographer that colored light reflected off of objects is what you're trying to capture.

There are times when scattered light in the sky contributes a lot of the light on the landscape, and reflections off of the objects you're viewing and off of dust particles in the air change the color of what you're trying to take a picture of.   The scattered light is changing the color of the objects in your scene, applying what you'll perceive as a color-reducing or color-muddying influence.  Fortunately reflected light is polarized, so you can use a polarizing filter to reduce the effect scattered light has on the scene, and reduce the interference it has with the colors in your shot.  Some people think of polarizing filters as "enhancing" a shot, when actually it's arguably more accurate to think of them as unmasking and enabling you to more accurately record the light and colors which already exist in the scene.

This ability of polarizing filters to help us better see a scene's color and reduced scattered and reflected light is why I recommend considering them as one of my top tips for landscape photography:

16 Tips for Better Landscape Photography
http://activesole.blogspot.com/2007/10/16-steps-to-great-results.html

Polarizing filters get somewhat of a bad reputation for working inconsistently across a wide section of blue sky, but there are a few simple characteristics you can understand about them and improve your success rate with them.  First of all, in the sky light is polarized most at angles perpendicular to the direction sunlight is coming from .  So if the sun is setting due west, the light being reflected in the sky is most polarized due north and due south.  Second, a wide angle lens covers a wide range of compass directions, so the polarization will be uneven across the sky it covers.  Once you understand these simple characteristics, you can watch for the negative effects in wide shots and remove the polarizing filter when it's creating undesirable effects, but still take advantage of polarizing filters when your focal length is longer (as in this image captured at 144mm) or when the light in a wider shot isn't displaying an objectionable range of uneven polarization, such as when you're shooting closer to directly towards or away from the sun and there's less strong and a lower range of polarization across the scene.

This image was taken during one of my recent landscape photography workshops in Yosemite National Park.  I recommend that photographers bring polarizing filters for their lenses, and it often surprises me how many have such a strong negative bias against polarizers that they either refuse to bring one on the trip at all, or they have them along but leave them in their camera bag back in the car when they set out to capture sunset shots.  If I have a compatible filter size I'll loan them one of mine, and they can see the difference for themselves.  That's one of the values of a photography workshop.  If you have an experienced and knowledgeable instructor, they can help you anticipate and uncover opportunities which you may overlook in your current shooting practices.  It's not that their approach is any "better" simply that if the really have been exploring a range of techniques full time for years, they can help you evaluate new approaches and  consider them when you approach given shooting situations, perhaps saving you the years it might take to go through a similar process of discovery and learning.

Anyone can take a few good pictures and offer a landscape photography workshop.   Not everyone has truly spent enough time in the field, and explored and mastered a wide range of situations and techniques, to have a lot to teach you.

Canon EOS 5D Mark III camera
Canon 70-200mm f/4 IS L Series lens at 155mm focal length
Marumi Super Cicrcular PLD filter
Sirui T-2205X tripod