vbnautilus 48 Posted May 15, 2008 Share Posted May 15, 2008 My theory is that it would be either 7 or 8. In speech class they tell you that you can only give the audience 7 ideas at a time (with some variation based on difficulty) before you lose your audience. So I think there is some fundamental property of the brain that is "seven-ish". Ten seems to work OK, but that may be just because we're used to it. Would base 7 be somehow more aesthetic? Would more people like math?Seven is the average number of items a person can keep in working memory at one time. I don't know about 'ideas' but you can generally hold about seven chunks of information in your verbal rehearsal loop without losing them. Usually we say 7 plus or minus 2 because there is some variability there, but I agree 7 is a reasonable base if you don't have some external counting mechanism like fingers to offload your memory onto. Link to post Share on other sites

Max_Powers 0 Posted May 16, 2008 Share Posted May 16, 2008 I’m ignorant about a few math concepts, and I’m having a bit of trouble imaging what a “base 7” counting system would look like. Base 10 refers to the fact that each place in our number system represents a power of ten, correct?So in base 7 each place is a power of 7? What’s the biggest number that can be written with two digits in base 7? At first I thought 77, then I thought 49, then 47, and now I’m not sure.EDIT: My newsest guess for the biggest two digit number is 56... which in base 7 would be written as 77... am I correct? Link to post Share on other sites

LongLiveYorke 38 Posted May 16, 2008 Share Posted May 16, 2008 I’m ignorant about a few math concepts, and I’m having a bit of trouble imaging what a “base 7” counting system would look like. Base 10 refers to the fact that each place in our number system represents a power of ten, correct?So in base 7 each place is a power of 7? What’s the biggest number that can be written with two digits in base 7? At first I thought 77, then I thought 49, then 47, and now I’m not sure.EDIT: My newsest guess for the biggest two digit number is 56... which in base 7 would be written as 77... am I correct?Understanding basis isn't that difficult. The idea is that a number is an abstract concept. If we're talking integers, then an integer certainly is independent of how we choose to describe it. If we consider every integer a little red block, then the amount of blocks are independent of how we describe them. So, if there are 10 little red blocks, then the concept of how many blocks there are doesn't depend on whether the number we use has two digits or one.So, bases work as follows:We pick a "base," which is just some number, and describe any other number in terms of that base. So, let's say that our basis is x. Any number then can be written as:a + b*x + c*x^2 + d*x^3 + e*x^4 + ....We can then invent a number system as follows: Choose a base, which is an abstract concept representing a certain number of things. Give that base a name (for instance, 10, 7, 12, or whatever). Then, come up with that base-1 other numbers (ie 1-9). Then any number can be written in the above fashion.The actual number then that we would use in conversation and writing then would be ...edcbaIf we're working in base 7, numbers are described asa + b*7 + c*49 + d* 343 + ...If we want a two digit number, we can only use a and b, so the biggest number that we can use is6 + 6*7 = 48 (which is clear since 7*7 is 49, just like 10*10 is 100 and 99 is the biggest two digit number).If you don't understand fully, just go through the above line by line and see how it works for base 10 and see how you replicate our current system of numbers. Link to post Share on other sites

runthemover 39 Posted May 16, 2008 Share Posted May 16, 2008 LLY, don't forget that the basis never gets the girls Link to post Share on other sites

strategy 4 Posted May 16, 2008 Share Posted May 16, 2008 YES!Even my wife found this facinating. If anyone ever runs across this in the future, watch it. It is amazing.I should be studying, but now I'm going to watch this instead. Thanks for ruining my GPA.http://video.google.com/videoplay?docid=82...08516&hl=en Link to post Share on other sites

qyayqi 11 Posted May 16, 2008 Share Posted May 16, 2008 I’m ignorant about a few math concepts, and I’m having a bit of trouble imaging what a “base 7” counting system would look like. Base 10 refers to the fact that each place in our number system represents a power of ten, correct?So in base 7 each place is a power of 7? What’s the biggest number that can be written with two digits in base 7? At first I thought 77, then I thought 49, then 47, and now I’m not sure.EDIT: My newsest guess for the biggest two digit number is 56... which in base 7 would be written as 77... am I correct?1 2 3 4 5 6 10 11 12 13 14 15 16 20 21 22 23 24 25 26 30 31 32 33 34 35 36 40... 64 65 66 100 ....in the same sense that 10x10-1 = 99 as the highest 2-digit base 10 number, 7x7-1= 48. so you count count to 48 base 10 (66 base 7) before you get to 49 base 10 (100 base 7). Link to post Share on other sites

hblask 1 Posted May 16, 2008 Share Posted May 16, 2008 OK, I understand base, and I had to wade through LLY's description. Let me see if I can simplify:Remember in school, we learned about "the ones column", and the "tens column" and the "hundreds column"? That's because we are base 10. The first column on the right is always "the ones column". The second column from the right, which in base 10 is "the tens column", in any other base X is "the X column". The next one is "the X*X column", then "X*X*X column", etc.To make it simple, let's stick with 4 digit numbers. In base 10, the columns are:1000s 100s 10s 1sSo a number like 4312 (base 10) = 4*1000 + 3*100 + 1*10 + 2*1 = 4312 (base 10)So in base 2 (binary), the columns are8s 4s 2s 1s.So a number like 1101 (base 2) = 1*8 + 1*4 + 0*2 + 1*1 = 13 (base 10)In base 7, the columns are:343s 49s 7s 1s4215 (base7) = 4*343 + 2*49 + 1*7 + 5*1 = 1482 (base 10)The thing to remember is that in base X you can never have a digit higher than X-1. In base 10, that means 9 is the highest. In binary, 1 is the highest digit. In hexadecimal (base 16), F is the highest digit.If we wanted to invent 1000 symbols, we could use base 1000, and the number 1010 base 10 might be written as !A base 1000.The other thing to remember is that if our default was base 7, there wouldn't be any converting, it would just seem as natural as our current system. It's just that the symbols would mean different things -- 10 would mean the count of this many things: * * * * * * * instead of this many: * * * * * * * * * *. And there would be no digit 8 or 9. Those digits wouldn't exist, just as we have no digit for 11 now.OK, upon rereading this, this explanation is no easeir to get through than LLY's, but since I bothered typing it, I'm posting it anyway. I thought this would make more sense to use concrete examples. Link to post Share on other sites

RhinestoneCowboy 2 Posted May 16, 2008 Share Posted May 16, 2008 1 is the magic number. It is the same no matter what base you use.SUCK ON THAT THREE!!! Link to post Share on other sites

Max_Powers 0 Posted May 16, 2008 Share Posted May 16, 2008 Thanks for the replys. I get it now. I figured out later that you would have no 7 in base seven just as we have no single digit for 10 in base 10. Its amazing that certain things you've thought of as concrete (such as base 10 counting) are actually completely arbitrary.I really have come to love math as I have gotten older. Math = truth. We humans just hang out arbitray notions on this truth and find ways to work with it. Link to post Share on other sites

fighter 4 Posted May 17, 2008 Share Posted May 17, 2008 Dear LLY Happy birthday Link to post Share on other sites

LongLiveYorke 38 Posted May 17, 2008 Share Posted May 17, 2008 That's pretty amazing. Now if you could somehow get that on a Fudgy the Whale, we'd really be in business. Link to post Share on other sites

LongLiveYorke 38 Posted May 17, 2008 Share Posted May 17, 2008 Dear LLY Happy birthdayThanks! I'm going to a Yankees/Mets subway series game and then I'm off to drink away about 10 years worth of education. So, someone be prepared to reteach me calculus tomorrow. Link to post Share on other sites

Napa_Don 688 Posted May 17, 2008 Share Posted May 17, 2008 No, no, none of this can be correct. It's all wrong. Link to post Share on other sites

Balloon guy 158 Posted May 17, 2008 Share Posted May 17, 2008 Thanks! I'm going to a Yankees/Mets subway series game and then I'm off to drink away about 10 years worth of education. So, someone be prepared to reteach me calculus tomorrow.Happy Birthday, here's a joke you can share at work:New York (CNN): At John F. Kennedy International Airport today, a Caucasian male (later discovered to be a mathematics graduate on his way home from his brithday party) was arrested trying to board a flight while in possession of a compass, a protractor, and a graphical calculator. According law enforcement officials, he is believed to have ties to the Al-Gebra network. He will be charged with carrying weapons of math instruction. Link to post Share on other sites

AmScray 355 Posted May 17, 2008 Share Posted May 17, 2008 Happy birthday. Link to post Share on other sites

LongLiveYorke 38 Posted May 17, 2008 Share Posted May 17, 2008 Happy birthday.Yeah, but how much can he grip? Link to post Share on other sites

AmScray 355 Posted May 17, 2008 Share Posted May 17, 2008 Yeah, but how much can he grip?At the very minimum, a cake... but wouldn't it be nice if he couldn't grip that cake?That's right... OOPS! make sure to cover yourself with that slippery, slippery cake that's just barely covering your long, strong manhood... Awwww, you're having a hard time with it? Let me come over there and help you... Link to post Share on other sites

LongLiveYorke 38 Posted May 17, 2008 Share Posted May 17, 2008 I like where this thread is going. Link to post Share on other sites

zimmer4141 0 Posted May 17, 2008 Share Posted May 17, 2008 What would happen if some supersmart scientist came in here and basically disproved all of LLY's claims throughout this whole thread? Wouldn't that be hilarious? Link to post Share on other sites

strategy 4 Posted May 18, 2008 Share Posted May 18, 2008 What would happen if some supersmart scientist came in here and basically disproved all of LLY's claims throughout this whole thread? Wouldn't that be hilarious?it would undoubtedly rip the universe a new black hole. Link to post Share on other sites

speedz99 145 Posted May 18, 2008 Share Posted May 18, 2008 I like where this thread is going.Funky Town? Link to post Share on other sites

runthemover 39 Posted May 18, 2008 Share Posted May 18, 2008 Take a train to Happy Town. woo woo!Rental Car Smells Like Sunshine!wrong order? so what Link to post Share on other sites

AmScray 355 Posted May 22, 2008 Share Posted May 22, 2008 http://whistleralley.com/planimeter/planimeter.htmHelpI need this thing called a "planimeter" to figure out approximate land areas on plat maps of old county real property records, but I don't understand how it works as it involves symbols and something called "Green's theorem". Link to post Share on other sites

## Recommended Posts

## Create an account or sign in to comment

You need to be a member in order to leave a comment

## Create an account

Sign up for a new account in our community. It's easy!

Register a new account## Sign in

Already have an account? Sign in here.

Sign In Now