Arithmetic Question

[FantWriter]

I write science fiction.

One of my ongoing projects (something to do whenever I'm avoiding working on a story) is what an alien grade-school primer might look like. I posit for this that the aliens weren't good at rote memorization but excelled at understanding and recalling concepts.

In doing the umpteenth restart-from-scratch, I've reached a point which has always made me uncomfortable.

After teaching numerals, the next obvious step is 1+1=2.

I'm really torn, though, on what should follow.

The choice I see is between 2-1=1 and 1+2=3.

There are valid reasons for each.

2-1=1 is complimentary to 1+1=2, and a concept is more readily understood when an opposing concept is
presented alongside.

1+2=3 expands the concept of addition before presenting totally new material.

Thoughts?

(I can't use human education systems as a guide because they are almost totally learning by rote, which the aliens didn't do well.)

One aspect which might affect judgment -- addition was presented, in a way, in teaching the numerals (combining a 1 and a 3 creates a 4, a 2 and a 3 creates a 5, etc.).

 

[J.R. Bob Dobbs]

the awnser is always 42



but to awnser you question i will say this...

When it comes to aliens anything is possible. With human beings there are circumstances where 1+1 does not = 2
http://mathforum.org/library/drmath/view/57110.htm
Math Forum - Ask Dr. Math
Carpe Diem - When 1 plus 1 is not equal to 2

have fun with that

 

[BWhare]

Our whole math system is based on learning by rote. Each number must be learned as a distinctive entity and values are then added to them.

A more simplistic and systematic method might be to simply use what's available. Take lines for example. You could take two vertical lines and add them together to build a two line figure that would make sense and wouldn't need to be learned by rote.

What I mean is: take the following letters to their most simplistic form because my keyboard won't do it for me and I don't feel like pulling out a graphics program and character mapping is no longer my forte ...

I is a vertical line without the top and bottom caps
I + I = L
I + I + I = U (a box without a top)
I + I + I + I = a box
a box + I = 0 (a circle)

So you have 1 thru 5 in pictograms kinda
6 thru 10 would be
OI, OL, OU, Obox and ∞ (really two circles, one beside another).

Logic can then be applied to introduce subtraction.

Unfortunately, this appears to be a simple base 5 system so it would end up being rather cumbersome eventually but at least it might demonstrate the basics of math without the necessity of long term memory.

Well... that's my take on it anyway ;-)

 

[FantWriter]

When it comes to aliens anything is possible. With human beings there are circumstances where 1+1 does not = 2

I'm reminded of the song "Cheap Lawyer" Frank Hayes. One verse goes:

Ask a housewife how much 2+2 is,
Without hesitation she'll tell you it's 4.
Ask an accountant, and he'll say he's fairly certain,
But let me run through those figures once more.
Ask a doctor, and he'll think about malpractice,
And he'll tell you that he's fairly sure at the very least it's 3
But ask a lawyer, and he'll lock the door and draw the curtains
And whisper to you "How much do you want it to be?"

 

[FantWriter]

A more simplistic and systematic method might be to simply use what's available. Take lines for example. You could take two vertical lines and add them together to build a two line figure that would make sense and wouldn't need to be learned by rote.

I'm trying the "strokes are numerals" method, in a way, for 1 and 2. Then positional notation for 3 and 6 (a lowered and inverted 1 means one group of three, a lowered and inverted 2 means two groups of three). 4, 5, 7, and 8 are combinations of 1, 2, 3, and 6.

I'm lousy at explaining it (which is a terrible thing for a writer to admit, but non-fiction has never been my forte).
Book One -- Page Set 001
(The font is still driving me crazy, and the CAD program I use doesn't generate image files, so it's a bit of a mish-mosh. On the other hand, I'm postulating explorers on another planet taking pictures of books they find and sending them back to Earth for analysis, so some level of "crude but discernible" is expected.)

The base? It's Base3 within the digits. Whole numbers could be considered Base8. The counting goes: 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22 . . ..

I'm trying to expand on the conceptual nature of their arithmetic by making the plus sign a stylized hook, the minus sign a stylized knife, and the equals sign a stylized hand (to hold out the result).

In previous runs at this, I've gotten up to a Fibonacci-like function (6F3 = 24 means the 6th number in a sequence beginning with 3 is 24. (3, 3, 6, 9, 15, 24)). Each time, I hit a point where I realize I should have standardized something early on, and going back to the story I should be working on is easier than starting over from scratch.

 

[Izan]

Fant,
consider the 1% or more! have fun

https://www.youtube.com/watch?v=rDRXn96HrtY

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