Hey all-
So I was laying in bed thinking about synesthesia and how one autist boy, Jake, described the way he thought of numbers as shapes..etc.

Now, I decided to see if I could practice that synesthesia- I started by squaring 3 - so I imagined in my head three 3's in a triangle like so (try to ignore the dots and lines):

...3
3....3

Then I squared it again and imagined the same triangle making up new corners of another triangle:
_______...3
_______3....3
...3___________...3
3....3__________3....3

And you simply add the threes. Thinking this way makes computing much easier.

Then I decided to subtract a fraction 5 - (1/3).
I imagined 5 circles, and I imagined 1 - (1/3) , which equals 2/3.
I simply replaced one of the five circles with the 2/3 and then re-added them to equal 4 and 2/3.

Then I decided to divide really large numbers by separating the digits spatially- so if I was going to divide 12,345 by 2 I would visualize the units, staring with five being the closest too me, and 10,000 being the farthest away. then I would compute each one easily.
5 / 2 = 2.5
40 / 2 = 20
300 / 2 = 150
2,000 / 2 = 1,000
10,000 / 2 = 5,000


Then add them up (2.5+20+150+1,000+5,000) = 6172.5

Its much easier than trying to do the long division crap...I dunno, it just seems like the way I was taught to do math didn't involve any spatial manipulating, but if it did, I would probably have gone further with it. I've always liked math, but I like it better this way.

Well, I just started doing it for a few minutes when I wondered- CAN I teach myself to do math in a different way (by manipulating numbers in my mind spatially)?

and also, CAN anyone else do this if they try? Would it come easier to aspies?

And then I thought- could this be an alternative way of teaching math if a person is capable of visualizing the numbers in a way that vastly simplifies the computing?

It would make it possible to compute very large values quicker and without a calculator/paper.

(who knows this could be the beginnings of creating that aspie-friendly research institute i mentioned- lol)

Your thoughts?

This post was last modified: 06-29-2012 10:00 AM by sg1008.

I think your unto something here, and I especially liked the way you used your imagination to do long division One thing though I was wondering was how do divide a large number like 12,345 by three instead of two? Not mocking your idea but I was just curious :/

With Military time, instead of subtracting 1200 from, say, 1900 I simply subtract 2 from 9 thus 1900 in 12 hour clock format equals 7 P.M. Since I already know 1300 hours is 1 P.M. in the 24 hour clock I can simply subtract 2 from 1400 hours (2) and so on.  

There's so many different ways of doing mathematical calculations

I think your unto something here, and I especially liked the way you used your imagination to do long division One thing though I was wondering was how do divide a large number like 12,345 by three instead of two? Not mocking your idea but I was just curious :/

With Military time, instead of subtracting 1200 from, say, 1900 I simply subtract 2 from 9 thus 1900 in 12 hour clock format equals 7 P.M. Since I already know 1300 hours is 1 P.M. in the 24 hour clock I can simply subtract 2 from 1400 hours (2) and so on.  

There's so many different ways of doing mathematical calculations

it is my impression that each number follows certain patterns or habits of dividing/multiplying/adding/etc, so in order to answer your question I would need to think about each number a bit longer to re-familiarize myself with its character.

Once I do that, and i can probably suggest more visuals.

I think it would be down to understanding the behavior of single digit numbers first (0,1,2,3,4,5,6,7,8,9), and once you understand them you can easily solve any math problem.... (is my theory)

I have to study the numbers a little longer....i but i really think arithmetic and algebra are super simple once you master the digits....(im not 100% sure, but i think...)

my dad knows an insane amount of tricks having to do with numbers...even higher up (like the number 11 for instance).
A good way to think out some patterns (if your interested) is to take a number (like 9), and create a list where you add it to each number
9+0=
9+1=
9+2=
etc...

try an discover the pattern.

Then multiply it
9*0=
9*1=
9*2=
etc..

and discover the pattern there.

Then keep doing tricks with the number 9, and numbers that are multiples of 9 (18, 27, 36, etc) and see if patterns continues.

Once you know so much about number 9, once you see it, you can guess how it will act if you have to divide it by 3- for example.
---

Do the same with each number. Discover their patterns. To give you a hint, many patterns are in the additive value of the fina value. For instance 9*2=18.... Look at 18 and you'll notice 1+8=9. Another hint, some final values are closely related to one of the values you used to add- for example, 9+2=11...Look at 11 and you'll notice 1+1=2 (the number two is what you just added to 9).

Some patterns are more obvious, such as any multiple of 5 will end in either a 5 or a 0. (5,10,15,20,25,30,35,40 etc).
Or, if you add two even numbers, it will equal an even number. If you add two odd numbers, it will also equal and even number. BUT if you add an even plus an odd number, it will equal an odd number.

Numbers are full of patterns a tricks...probably why many autists/aspies like math/engineering/physics etc.

This post was last modified: 07-01-2012 12:55 AM by sg1008.

I've been studying about the way how Binary has a lot of common ground with the Roman Numerals lately, and I notice some similarities between the two.

I II III VI V VI VII VIII IX X  
01 10 11 100 101 110 111 1000 1001 1010
                                                              
I've been noticing the way the zero, after 4, moves to it's common place after 11 :/  Common place in my terms is the way the zero is mostly on the right side after four.  

Also I've noticed the ones and zero's look like they're almost playing a game of leap frog. But I know it's the way data stacks itself, like someone with three wooden blocks moving the bottom to the top and etc in some sort of juggling motion....

interesting....sometimes I wish I had 100 heads so that I could designate each one to spend its life thinking about a different interest.

Is that a good thing or ...... ?

On second though, never the *** mind. I'm sick of loaning my opinions and thoughts on something, only to end up getting people pissed off at me.....

You lost me after "Hey"!  However, it's my fault, since I'm totally dyscalculic.  I was hopeful that I'd somehow "get" math when I started Japanese and found that all the numbers are represented by characters.  But unfortunately the basic concept of math once again just flowed out of my mind like water through a sieve.  I just can't hold numbers in my head long enough to do anything ueful with them.  But the written word is a totally different thing, and I adore that!  I always think my hyperlexia co-opted the part of my brain that should have dealt with math, leaving me with a massive affinity for the written word but a great deficit for numbers.
Alison

This post was last modified: 07-01-2012 02:59 AM by Alison.

I do similar operations in my head, but in bigger chunks, when I do my "instant calculator" tricks.

Say if someone asks what is 99 * 47, the answer is simply 4700 - 47 = 4653.

Say someone wants to know 4691/8, the answer is 600 - 109/8 = 600 - 13.75 = 586.25.

It isn't something I ever gave much thought to, just something I found I could do in my teens. The only time I gave it much thought was when someone gave me a hard time for not being able to give calculator style answers for division by 7, hence my username.

what do you mean?
It was interesting what you pointed out. Thats all I meant..and then I expressed the desire to have more heads (because I thought it would be nice to focus on learning math, and binary code, but an extra head would be make it more possible lol).

You didn't piss me off or anything....? Im a little confused :/

I took a spanish linguistics class in Peru and outperformed all the native speakers because I found linguistics to be just like math...and loved it. Perhaps you do know math- but in language-format lol

Haha cool! would you mind sharing more of your calculator tricks?

If you want 63 * 28 it gets a bit harder.

First I would do 60 * 20 = 1200. Then 60 * 8 = 480. Then 3 * 28 = 84.

Keep a running total as you go. You get 1764.

Each operation takes about one second. So you can actually work it all out while repeating the question back to them. So as soon as they ask I repeat back "sixty three times twenty eight equals" and I already have the answer. It sounds like you did it in one hard step, but actually you broke it into 3 steps.

Division by 7 is most impressive. Say you are in a restaurant and the bill comes to $238.60. 7 into 210 is 30, leaving 28.60. 7 into 28 is 4. The 7 into 60 cents is 8.57142857 and so on. The decimals are always the same sequence of recurring numbers and all that changes is the number you start with. In this case the remainder was 4/7, so that always starts with the 5.

So you give an answer of 34.08.57142857.... Before anyone else at the table can get their calculator or smartphone out.

Another trick is to give a close estimation right off. Then you say "that is to the nearest dollar, is that okay, or I can give you the exact figure which is....". This gives you plenty of time to do the harder calcs and it still sounds like you pulled the number off the top of your head.