My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 20th, 2008, 01:27 PM   #1
Member
 
Joined: Apr 2008
From: New York

Posts: 41
Thanks: 0

I count in base 11

Since I have ten fingers it seems as though I should be able to count ten objects before I need to use "another digit". Isn't this base 11? If my lefthand thumb is number 1, and my lefthand pointer finger is number 2 why does my righthand thumb get to have two characters (10)? Was the first number theorist "missing something" or am I counting something I shouldn't?
oneandone is offline  
 
May 20th, 2008, 03:07 PM   #2
Senior Member
 
Joined: May 2007

Posts: 402
Thanks: 0

And what if your first finger was 0?
milin is offline  
May 20th, 2008, 08:55 PM   #3
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
You can count on your fingers many different ways. Perhaps you can't control your pinky/last finger too well, so you only have an effective 8 digits, but you use these as binary indicators. Now you can count to 256 (or 255 if you start with 0) on your fingers.
CRGreathouse is offline  
May 21st, 2008, 11:52 AM   #4
Member
 
Joined: Apr 2008
From: New York

Posts: 41
Thanks: 0

This entire query probably has more to do with psychology than mathematics, but I still wonder....

If I'm a neandrethal mathematician, and I start a collection of objects I'm not going to consider my initial object to be the zeroth. I can match each object with a finger until I get ten objects. If I get another object I need to put a mark in the sand, use a toe, or call over a colleague to put up a finger. This should be where I invent the number "10" with the "1" meaning "I have used up all of my fingers once". At this point I have eleven objects.

Most of us use the symbols 1 2 3... instead of our fingers to count things today. It seems curious that there is no unique symbol for "my righthand thumb". Most people use the symbol, and concept of, 0 to mean "no fingers at all".

Presumably if we had a different number of fingers we would use a differently based number sysyem. Why do we use base 10 instead of base 11?

I know that "curious" ideas shouldn't be dismissed in mathematics. Just look at my elastic numberline post (which I'm still working on). After seeing the movie "Beautiful Mind" my wife thinks that mathematics leads to insanity. Is there any truth to this?
oneandone is offline  
May 21st, 2008, 12:24 PM   #5
Senior Member
 
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

It's an interesting question, although it seems to be more of an anthropology or philosophy of mind question than mathematics.

Quote:
Originally Posted by oneandone
I know that "curious" ideas shouldn't be dismissed in mathematics. Just look at my elastic numberline post (which I'm still working on). After seeing the movie "Beautiful Mind" my wife thinks that mathematics leads to insanity. Is there any truth to this?
Actually, I think her causality is backwards: Insanity leads to mathematics
Although I may be (and probably am) wrong here, there does seem to be a slight correlation between mathematical aptitude and various mental illnesses; the most notable of which (although definitely not the one with the strongest correlation) is schizophrenia.

If I were to venture a guess as to the cause of (#1) the correlation between intelligence and mental problems and (#2) the correlation between intelligence and schizophrenia specifically I would say:

#1 is probably associated with the fact that those of greater intelligence have more trouble associating with "normal" people, who have a very different thought process. Therefore, they develop social anxieties, withdrawing from society (hence making the problems more acute).
I know for myself, as "social" as I am (especially for a nerd), I get really, really, really nervous in large groups, and around people I don't know.

For #2: Whatever it is that allows a person to think abstractly quite likely also causes them to lose grasp of the real world.
viz, being able to abstract away from what we "know" to something new (i.e. mathematical aptitude) also causes us to abstract what we see to a different experience (i.e. schizophrenic episodes).
cknapp is offline  
May 21st, 2008, 02:03 PM   #6
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Quote:
Originally Posted by oneandone
Presumably if we had a different number of fingers we would use a differently based number sysyem. Why do we use base 10 instead of base 11?
Since I'm into linguistics, I'll mention here that the most common bases are probably 10, 20, and 5, in that order. The number of digits on a hand/both hands/hands and feet seems to be the deciding factor; in many languages some small numbers are etymologically related to words for fingers/hands/etc. I've heard that the Proto-Indo-European *pengke, the root for our "five", may have a similar background -- though I don't think that's well accepted.
CRGreathouse is offline  
May 25th, 2008, 06:37 AM   #7
RAM
Newbie
 
Joined: May 2008

Posts: 1
Thanks: 0

Fingers arent the only reason for a culture using a certain base. The ancient babylonians used base 60. Popular theory is because it's the smallest number divisible by 1,2,3,4,5,and 6. The current base system might even change in the future. Binary could get alot more popular due to its use in computers.
RAM is offline  
May 25th, 2008, 03:05 PM   #8
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Quote:
Originally Posted by RAM
Fingers arent the only reason for a culture using a certain base. The ancient babylonians used base 60. Popular theory is because it's the smallest number divisible by 1,2,3,4,5,and 6. The current base system might even change in the future. Binary could get alot more popular due to its use in computers.
Yes, base 60 (actually split case 10-60), base 12, and base 100 (split base 10-100) were also used, but they were less common than the ones I mentioned above.

A direct use of base 2 is unwieldy, but base 8 or 16 is easily convertable.
CRGreathouse is offline  
May 28th, 2008, 12:14 PM   #9
Newbie
 
Joined: Oct 2007
From: The Netherlands

Posts: 1
Thanks: 0

I would like to return to the first post by noting that with ten fingers, it actually is most logical to use the base 10 system we are using. This gets more obvious if you continue counting for more 10-cycles. Say you do represent 10 with a new symbol, say A. Then the first 10 counts would be 1,2,3,4,5,6,7,8,9,A. After that, you would continue with 11 (not 10, that would mean creating a new symbol 0), 12,13,14,15,16,17,18,19,A,21,22.....
As you can see, this just replaces a symbol, it doesn't create a new base. If you would, however, create a base 11 system, counting would soon get out of sync with your fingers. Just try counting 1,2,3,4,5,6,7,8,9,A,10,11.... on your fingers.

But this is probably pretty much what milin already said by pointing out that your first finger could be 0.[/list]
Florian is offline  
May 28th, 2008, 01:37 PM   #10
Senior Member
 
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

Ah, but what if, as the op suggested, you place a stone (or other marker) on every 11th number?

That is, count 1-A, then drop a stone on B, then start again with 1. The act of dropping the stone (on the 11th number) will also reset your fingers (to 0). Using a base-10 system, using all 10 fingers and "un-using" your hands are the same action; if it were 2 actions, there would be 1 extra digit in the number system.
cknapp is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
base, count



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How to count matrix 4x3 + 3x4 ? lauznisg Linear Algebra 2 February 19th, 2012 02:56 PM
What was the bacteria count at 10 am on Feb. 3? abyad Calculus 10 February 6th, 2012 07:41 PM
Base Conversion - Negative Base Tapas Bose Number Theory 10 August 6th, 2010 12:07 PM
Finding smallest n : (base^n + base^(n-1) + ... base^1) > x momesana Algebra 4 December 3rd, 2009 06:13 PM
Convert 324 from base 5 to base 10 rune2402 Elementary Math 4 November 9th, 2007 06:03 PM





Copyright © 2018 My Math Forum. All rights reserved.