Hmmm..
The pixs do not seem to be displaying in the last post. Why must this be difficult?
If I cannot make this work, what would happen to any chimpanzee that tried to blog about the Life Primeval?
It would be disappointed, friends. Disappointed and unable to display its homely visage.
Differences:
Take this series of numbers; 1,2,3,4,5,6,7,8,9,10.
Each of these numbers is different from the previous number by the same amount: 1.
So the series of first differences for this series is 1,1,1,1,1,1,1,1,1.
And the series of second differences is 0,0,0,0,0,0,0,0,0
Its boring. While manipulation of differences can be useful - the Difference Engine after all was not a machine designed to generate social alternatives - its seems to be a rarely used tool in the mathematics toolbox. However its a simple enough tool for my poor brain to understand. Lets try a better series.
The first ten thousand prime numbers:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 ...
Bear with me, I'm coming to a point.
The first differences:
1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2
4 2 4 14 4 6 2 10 2 6 6 4 6 6 2 10 2 4 2 12 12 4 2 4 6
2 10 6 6 6 2 6 4 2 10 14 4 2 4 14 6 10 2 4 6 8 6 6 4 6
8 4 8 10 2 10 2 6 4 6 8 4 2 4 12 8 4 8 4 6 12 2 18 6
10 6 6 2 6 10 6 6 2 6 6 4 2 12 10 2 4 6 6 2 12 4 6 8
10 8 10 8 6 6 4 8 6 4 8 4 14 10 12 2 10 2 4 2 10 14 4 2
4 14 4 2 4 20 4 8 10 8 4 6 6 14 4 6 6 8 6 12 4 6 2 10
2 6 10 2 10 2 6 18 4 2 4 6 6 8 6 6 22 2 10 8 10 6 6 8
12 4 6 6 2 6 12 10 18 2 4 6 2 6 4 2 4 12 2 6 34 6 6 8
18 10 14 4 2 4 6 8 4 2 6 12 10 2 4 2 4 6 12 12 8 12 6 4
6 8 4 8 4 14 4 6 2 4 6 2 6 10 20 6 4 2 24 4 2 10 12 ...
Now this seems to be patterned. The pattern reminds me of a wave form with increasing amplitude and decreasing frequency. Also note the new series ..... remove the redundancies and you end up with
One could also ignore every number in the series that is less than the previous number. This generates
2,4,6,8,10,12....
The set of primes having been proved infinite, I wonder if this means that this subset of differences is also infinite, containing within itself all integers that are a multiple of 2...
I would like to graph this, but tonight I've managed to crash Excel three times, and Quattro wasn't any better at handling it. I would think that a 2.2 Ghz processor with 512 MB of RAM could graph a measly 9,999 data points, even with Micro$oft bloatware...
I'll have to find a better program , and one that preferably does not require two hours of study in order to produce a stinkin' graph. If I was going to bother to learn something, I'd figure out how to do this in Mathematica.
I was going to be a bastard and post all 10,000 primes and 9,999 differences, but that seemed anal. I've uploaded both and here are the links:
First Differences
Second Differences
And , of course the primes:
(Ever notice that there is not a word for 'all three'?
I hereby coin 'Throce' to fill the void...)
Now for the second differences:
1 0 2 -2 2 -2 2 2 -4 4 -2 -2 2 2 0 -4 4 -2 -2 4 -2 2 2 -4 -2 2 ...
Note the negative numbers. This causes a fork in the inquiry. It was the negatives that led me to visualize waves in the first place. If I calculate the differences using absolute values, I get:
1 0 2 2 2 2 2 2 4 4 2 2 2 2 0 4 4 2 2 4 2 2 2 4 2 2 ...
and third differences:
1 2 0 0 0 0 0 2 0 2 0 0 0 2 4 0 2 0 2 2 0 0 2 2 0 0 ...
Amused myself in using the first differences to create a bitmap. Copied a BMP header onto the textfile using DOS EDIT in binary mode; used Find/Replace to deal with the pesky CR/LF characters (that's Carriage Return/Line Feed, a beautiful vestige of the teletype, btw ) ; and then took a peek with photoshop:
The aspect ratio is completely arbitrary. Its a little gray.
I tweaked it a bit, boosted the contrast as high it would go for the pleasant polychrome effect:
Now, if I was feeling progressive, I'd get the computer to generate several thousand copies at various aspect ratios that I could page through and see if any patterns emerged. But not tonight - I'm tired, see?
Take this series of numbers; 1,2,3,4,5,6,7,8,9,10.
Each of these numbers is different from the previous number by the same amount: 1.
So the series of first differences for this series is 1,1,1,1,1,1,1,1,1.
And the series of second differences is 0,0,0,0,0,0,0,0,0
Its boring. While manipulation of differences can be useful - the Difference Engine after all was not a machine designed to generate social alternatives - its seems to be a rarely used tool in the mathematics toolbox. However its a simple enough tool for my poor brain to understand. Lets try a better series.
The first ten thousand prime numbers:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 ...
Bear with me, I'm coming to a point.
The first differences:
1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2
4 2 4 14 4 6 2 10 2 6 6 4 6 6 2 10 2 4 2 12 12 4 2 4 6
2 10 6 6 6 2 6 4 2 10 14 4 2 4 14 6 10 2 4 6 8 6 6 4 6
8 4 8 10 2 10 2 6 4 6 8 4 2 4 12 8 4 8 4 6 12 2 18 6
10 6 6 2 6 10 6 6 2 6 6 4 2 12 10 2 4 6 6 2 12 4 6 8
10 8 10 8 6 6 4 8 6 4 8 4 14 10 12 2 10 2 4 2 10 14 4 2
4 14 4 2 4 20 4 8 10 8 4 6 6 14 4 6 6 8 6 12 4 6 2 10
2 6 10 2 10 2 6 18 4 2 4 6 6 8 6 6 22 2 10 8 10 6 6 8
12 4 6 6 2 6 12 10 18 2 4 6 2 6 4 2 4 12 2 6 34 6 6 8
18 10 14 4 2 4 6 8 4 2 6 12 10 2 4 2 4 6 12 12 8 12 6 4
6 8 4 8 4 14 4 6 2 4 6 2 6 10 20 6 4 2 24 4 2 10 12 ...
Now this seems to be patterned. The pattern reminds me of a wave form with increasing amplitude and decreasing frequency. Also note the new series ..... remove the redundancies and you end up with
One could also ignore every number in the series that is less than the previous number. This generates
2,4,6,8,10,12....
The set of primes having been proved infinite, I wonder if this means that this subset of differences is also infinite, containing within itself all integers that are a multiple of 2...
I would like to graph this, but tonight I've managed to crash Excel three times, and Quattro wasn't any better at handling it. I would think that a 2.2 Ghz processor with 512 MB of RAM could graph a measly 9,999 data points, even with Micro$oft bloatware...
I'll have to find a better program , and one that preferably does not require two hours of study in order to produce a stinkin' graph. If I was going to bother to learn something, I'd figure out how to do this in Mathematica.
I was going to be a bastard and post all 10,000 primes and 9,999 differences, but that seemed anal. I've uploaded both and here are the links:
First Differences
Second Differences
And , of course the primes:
(Ever notice that there is not a word for 'all three'?
I hereby coin 'Throce' to fill the void...)
Now for the second differences:
1 0 2 -2 2 -2 2 2 -4 4 -2 -2 2 2 0 -4 4 -2 -2 4 -2 2 2 -4 -2 2 ...
Note the negative numbers. This causes a fork in the inquiry. It was the negatives that led me to visualize waves in the first place. If I calculate the differences using absolute values, I get:
1 0 2 2 2 2 2 2 4 4 2 2 2 2 0 4 4 2 2 4 2 2 2 4 2 2 ...
and third differences:
1 2 0 0 0 0 0 2 0 2 0 0 0 2 4 0 2 0 2 2 0 0 2 2 0 0 ...
Amused myself in using the first differences to create a bitmap. Copied a BMP header onto the textfile using DOS EDIT in binary mode; used Find/Replace to deal with the pesky CR/LF characters (that's Carriage Return/Line Feed, a beautiful vestige of the teletype, btw ) ; and then took a peek with photoshop:
The aspect ratio is completely arbitrary. Its a little gray.
I tweaked it a bit, boosted the contrast as high it would go for the pleasant polychrome effect:
Now, if I was feeling progressive, I'd get the computer to generate several thousand copies at various aspect ratios that I could page through and see if any patterns emerged. But not tonight - I'm tired, see?
I was given a broken Vivatar 3826 Digital Still Camera. Its previous owner had smashed the lens off of it - accidently, I assume, and not in a fit of pique. Its names a misnomer, because it can take video as well. That capacity didn't excite me as I shoot very little video, and still use a old VHS camcorder. (Yes I know, its archaic technology, and not quite old enough yet to be hiply retro.)
I adapted a SLR camera lens to it. Most of my lenses are 52mm screw mount, so I cut down a screw on lens cap and glued that to the body of the camera after working out what seemed like the best spacing.
The flash was broken, so I unplugged the flash's circuit board and removed it. I had to cut the power leads to the flash board. The camera did not seem to care. Apprantly, it uses a timer to geuss when the flash capacitor is at full charge rather then some sort of feedback. Makes sence really:
the RC constant of the charger should only vary slightly, and within
acceptable bounds.
removed the tiny moter that drove the internal zoom lens. This moter is the size of a pencil eraser and will prove quite useful for another project. The big moter (I use the term loosely) that drove the focusing I didn't bother to remove. I just used a sharp X-Acto knife to cut the flexible circuit traces that led to it. I was going to leave the moters in, but they tended to move when I pressed the shutter button due to an irritating 'focus' setting before the switch could move to 'shoot'. This would vibrate the CCD when I wanted itI still.
Shooting indoors with on 30 watts of Compact Flo
urescent for light - a dim enviroment
- the camera did better than my unmodified Kodak EasyShare 7300. This is probably due to the much larger lens aperture.I then tried to take a shot outside, with a sunny background:
Massive overexposure!
Trying all availible settings of f-stop and exposure time didn't help. The camera was designed under the assumption that it had the light gathering ability of a 6 mm wide lense, and I was feeding it through a 40 mm wide lens.
Thats around a 44 X increase in light gathering!
Useful at night, I suppose, but not very useful for garden parties.
I used a old amateur astromer trick to solve that problem. I blocked the mouth of the lens with duct tape, and used a washer as a makeshift diaphramn. This brought the apeture down to around 5 mm and the overexposure became a thing of the past.
It does make the camera look odd, though.
Next step is to put a new and improved shutter switch on it. The original one takes too much force, and I don't like its action.
Subscribe to:
Posts (Atom)
