I am planning to write a series of articles on the way I have seen numbers through my life. This is the first post in that series.
In these posts I will try to be as logically accurate as possible. However, at some points the logic may appear fuzzy. At this point, I would recommend to lay back and enjoy the beauty in the patterns. Get a little philosophical. Also, you might find some of these observations in number theory/vedic mathematics(which ironically has nothing to do with the Vedas). My arrogance has prevented me from studying these, however, if you notice some similarity, let me know. Finally, do not think to much in mathematical terms of x and y, you will destroy the beauty.
The title of this post was inspired by this post by Karthik, which caused a lot of controversy. I do not agree that you can just move the number line randomly to any position, however, there is a slightly more logical way of showing similarities between zero and infinity.
To put it in fuzzy mathematical language, there are certain series of numbers, which as you go higher in series, exhibit zero-like behaviour.
To start of, consider the number 1000. Observe how the last three numbers are zero. Now, because of these zeros, 1000 exhibits some zero-like behavior. Now if 1000 is like 0, then 1001 would be like 1. Now 1001x2= 2002. The last three digits are 002. This is 1x2=2. Thus, if we consider only the last three digits, then the number 1000 exhibits zero-like behaviour for positive multiplication. Now let us look at some more properties. Similar pattern is observed while scoring,
1001^2 = 1002001,
again if we consider only the last three digits, we could be squaring one.
Now let us look at one more interesting property we see around 0 on the number line. Which is -1x-1 = 1. Now, around 1000, (1000-1)*(1000-1) = 998001. Again, for the last three digits, the behaviour is zero like. You can extend this logic to other simple multiplications like -1x1 =1, -2x4 = 8, etc.
Now, consider the series 10,100,1000, 10000 etc as we go higher up the series, we can find this pattern for more and more number of digits. Thus higher up in the series, numbers will exhibit higher degree of zero-like behaviour. Thus further we move from zero, more zero-like the number becomes. Strange?
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4 comments:
hmm
i'm not sure what to say exactly. i mean "zero like behaviour"??
what does it signify exactly?
As many zeroes as you add between the most significant digit and the units place, it will behave like the units place for some computations. For ex, 100000000003 will behave like three for the last 4 digits to a certain extent, until the higher bits catch up.
But I am unclear as to where this is leading to.
i hope it becomes clearer in the next post.. It does not lead to anything new that will be different from anything you already know but i find the pattern intriguing..
Sad the thing about Tendulkar. I read in the paper and said to myself tendulakr is dead leading to all surrounding ppl to think of sachin. :P
I was left a little dry after reading his Ghashiram Kotwal,, The translation was not good but even then i could see what a spectacle this play would be on stage, with all the dancing and all.
Interesting idea. I like the vedic guys idea much better still. :P
waiting for next post. Blogging has done ur writing a lot of good for sure.
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