Mathematical Education

During a college vacation, I strolled around my old grade school. The one teacher from my era who was still there spotted me, and remembered my interest: "Would you like to sit in on a math class?" Of course I would.

The teacher was fine with that, so I sat inconspicuously in a back row seat and paid attention. He was instructing his charges in New Math--the Binary System: how to express all whole numbers using only the digits one and two.

I kept waiting for some little Karl Friedrich Gauss to ask, "Sir (yes, back then we called them "Sir" and "Ma'am"), how to you express zero?"

I held my peace and thanked him when I left. They'd figure it out when they got to M.I.T.

(I may have been careless here, but here is my quickie judgement as to his otherBinary (oB) numeration:

 Base 10:         0 1 2 3 4 5 6 7 8 9 10 11 12
 Ways, base oB:   0 1 1 1 1 1 1 1 1 0  0  1  1
)

5 comments:

  1. Binary is always on and off, except it allows for frames of information (as well as subframes and superframes, depending upon the time structure; the frequency), such that the on/off structure produces a code, much more robust than what simple base numbers could produce.

    I've dealt with other standards when it comes to electrical commands, but almost always it comes down to whether the gate is open or closed (this is true even of analog systems). When dealing with more complex structures, such as hex, it just becomes too difficult to fit the information into a single packet, thus you must further create different sets of commands, or additional packets of info, just to perform a simple procedure. With binary, it is all + vs -, there is no need for this.

    I don't think that your example really shows anything significant, at least not in how binary is actually used, because you're simply using an "on" as an additive function, and then using the base of 10 as zero, without indicating time or sequence (as binary requires). In a real application, 9 would be not zero, but 9 would be a sequence of both ones and zeros (1001), thus it would be a code, not a number.

    Binary is surely an additive code (each command is a sequence of ones and zeroes, added to the other in that construct), but not in the way that you're using it (attempting to use an "on" or a "naught" indicator to show a distinct number).

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    1. Joe, Wabulon was programming back when you actually programmed IN binary with toggle switches.

      I think he is just trying to figure out what the teacher was thinking of.

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    2. Oh, okay. I was just confused as to how he was coming to that set. I'm looking at it and it makes no sense to me.

      In the Navy I was a sonar tech, and while most people aren't aware of this, in the surface fleet much of the sonar equipment is based upon 70s technology coupled with some newer tech (if it works don't fix it, they say). So I have done the toggle switch dance, but that was usually with hex rather than binary.

      It was really screwy though, because when dealing with integrated systems (of 20 discrete systems) that all speak different languages you often have to convert, and this gets even more hairy when troubleshooting because you have to do it super fast and usually in a sleep-deprived state.

      I got to be pretty awesome at understanding computer language and mathematical computation, but I am admittedly out of practice.

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  2. As far as I know, a single "0" is always and forever zero in binary language (emphasis on the word "language"). The only time that this is not true is if it is part of a frame or packet, in which case we are dealing with other numbers other than zero.

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