Random maths

[davenportram]

Well, using your hands to count to 1023 is takes a little practice but can be useful.

The concept is fairly simple, picture your fingers as representing either a 0 (down) or 1 (up) and use that as a number.

Hold your fingers up and think of your leftmost as the starting point (or the rightmost if you prefer).

1: 10000:00000

2: 01000:00000

3: 11000:00000

4: 00100:00000

5: 10100:00000

6: 01100:00000

7: 11100:00000

8: 00010:00000

The general rule is basically:

1. To add one add one to the leftmost place

2. If the leftmost place is already at one, make it into a 0

3. If the above is replacing a one, add one to the next place

4. If adding another one, and the next position is a one, then make it a zero and add one to the next place

5. Repeat the above

At the end add up the fingers as follows:

1 2 4 8 16 : 32 64 128 256 512

Add up the number you get times the above. For example:

10111:10110

1+4+8+16+32+128+256 = 445

This can of course lead to unfortunate combinations. 132 for example...

Albert that's a bastardised binary on your fingers. True binary is the other way round with the 1 Column on the right.

.... 64. 32. 16. 8. 4. 2. 1.

[Albert]

So long as notation is self consistent and understood it really doesn't matter. As said in the post, if you feel more comfortable counting from the right, that's all well and good, it's about what you're happy with. At the end of the day I personally use it from the left, hence I explained it that way.

Now, don't get me started on ternary fingers, that's a tad more complex to learn.

[-JW-]

Oh ffs.

[davenportram]

So long as notation is self consistent and understood it really doesn't matter. As said in the post, if you feel more comfortable counting from the right, that's all well and good, it's about what you're happy with. At the end of the day I personally use it from the left, hence I explained it that way.

Now, don't get me started on ternary fingers, that's a tad more complex to learn.

It does matter because the accepted convention and notation is to have the columns as I described.

If you used your notation everytime you used it you would have to have to explain it to whoever you showed your work.

It's like writing x2 to represent x squared, and saying its okay because I do it that way everytime.

[Albert]

Oh ffs.

If it's any worse, it's 4 am odd where I am.

[davenportram]

Or writing 21 to represent 12 when counting in base 10

[Albert]

It does matter because the accepted convention and notation is to have the columns as I described.

If you used your notation everytime you used it you would have to have to explain it to whoever you showed your work.

Actually, the way I use binary fingers is better as people see the numbers I am counting the right way. That is, 21 is seen as: 0000010101 from someone watching me. Whist to me it is 1010100000, it's obviously the other way around to someone seeing my hands.

...and of course I'd never write it the other way around in proper mathematics, this is about a simple hand system to do simple counting as to allow the user to count to 1023 instead of 10. If you're really bothered by the way presented, you can of course start from the right, it's simple enough.

[davenportram]

Ah but in your first post you said

011 in binary was the same as 12, without the caveat of it being the finger counting or explaining your notation. So that's why I was confused as it should be 3

[Albert]

Or writing 21 to represent 12 when counting in base 10

So long as notation is well explained and self consistent I have no issue with it. If you started with:

For the following ABCDE... is equal to A*1+B*10+C*100+D*1000*E*10000+... I'd be perfectly fine with it. Of course I'm not one to use the standards of my hand signals to dictate how I write formulae and such but hey...

[Albert]

Ah but in your first post you said

011 in binary was the same as 12, without the caveat of it being the finger counting or explaining your notation. So that's why I was confused as it should be 3

Direct quote please. I can't quite find where I said that.

[davenportram]

But the whole point if mathematics notation is to give a way of communicating consistently. As a purist I like to see standard notation and consistency. The decimal number system convention is to increas pace value from right to left, and so to with binary.

Similarly I hate the way what we call trapeziums in the uk are called trapezoids in America.

[davenportram]

It's impressive to me. You're a quantom thingymajig!

Just reading a guide (for binary) now, interesting!

2 to the power of x = x (2^x)

I could probably work those out.

2 to the power of 1 = 2 (2^1)

2 = 4 (2^2)

3 = 8 (2^3)

etc..

011 = 12.

0101 = 20 etc..

There you go. You also forgot 2^0=1

(The ^ is standard notation for to the power of)

[Albert]

There you go. You also forgot 2^0=1

(The ^ is standard notation for to the power of)

I'm sorry, but that wasn't me posting that. Look at the poster.

But the whole point if mathematics notation is to give a way of communicating consistently. As a purist I like to see standard notation and consistency. The decimal number system convention is to increas pace value from right to left, and so to with binary.

Similarly I hate the way what we call trapeziums in the uk are called trapezoids in America.

Again, I feel I made the notation fairly clear from the start. It's a matter of convince. If you do see yourself as a purist, then don't copy me, count the "proper" way on your hands. If you really want, count from the outside in. No, don't mind me, but my cats are apparently hungry.

[DCFCfranco]

??????????

[davenportram]

I'm sorry, but that wasn't me posting that. Look at the poster.

Again, I feel I made the notation fairly clear from the start. It's a matter of convince. If you do see yourself as a purist, then don't copy me, count the "proper" way on your hands. If you really want, count from the outside in. No, don't mind me, but my cats are apparently hungry.

Sorry Albert, I got confused because of all the binary and both of you appearing to make the same common mistake.

Purist I may be but convention is there for a reason.

[Albert]

??????????

Long story short, it's 4am where I am and I'm so drunk I doubt I could stand up, and davenportram who I have great respect for (rightly or wrongly) is quoting blackandwhites (who I have a measureable standard of respect for) as me. Long story short, you could use binary as a number system on your hands to count. Honestly, if you have any questions about maths right now, regardless of how "hard" they are, I could answer them right now if you want, as I'm likely to be awake for awhile now.

[Albert]

Sorry Albert, I got confused because of all the binary and both of you appearing to make the same common mistake.

Purist I may be but convention is there for a reason.

It is, but please keep in mind that I am one of those crazy few who challenges convention in his work, and put bluntly if I think something is easier for the layman, I'll tell them. You're right that convention is there for the a reason, but how many people know binary properly out of the population, and how many will potentially benefit from learning a "bastardised" version for counting?

Long story short, I spend my days working with a non-linear 3-rd (4th without a nice approximation) order differential equal with put bluntly, is like herding cats covered in bees and using binary hands in the way I do is nothing more than convenient.

[RamNut]

Why are you in australia?

How come when you get pissed you think about binary numbers?

Its all too bizarre?

[davenportram]

Fair enough Albert - I doubt that many people really benefit from learning Binary at all. A bit like Pythagoras really

[Albert]

Why are you in australia?

How come when you get pissed you think about binary numbers?

Its all too bizarre?

Why Australia? Family and PhD work. Why do I think of binary numbers and such when pished?

...I don't actually know. I wrote the whole "Nigel in numbers thing" off my face beyond words as well. Put bluntly, I don't like my life in recent months, but apparently alcohol makes me think 'deep thoughts'. Once drunk I tend to discuss what's going on in my head, and someone asks, I'll just throw out what I'm thinking normally.