## Tuesday, November 25, 2008

### ...to AbbyLeever on my classical Greek logarithms

AbbyLeever wrote:

This is a forest and the trees argument. It is like saying there really aren't any words in the english language, just the 26 letters. This is proven by the fact that whatever "word" you claim exists can be expressed by a certtain combination of letters.

I haven't claimed there are no numbers. I have claimed and still claim there are no numbers except the natural numbers. The 10log of two is not a number, it is a fictitious ratio between the exponents of ten and of two were the potencies are equal. Fictitous precisely because no potency of ten can be equal to any potency of two - that would involve one & the same number having two different sets of prime factors, one with only twos and another with an equal amount of twos and fives.

OK. That is not the kind of proof of nonsensity that would make all the words in English nonsense. Get it?

You can take any number there is and express it as a fraction just by going out to the point where you run out of decimals in your calculations from old age - each number expressed as a denominator with base 10 to some horrendous power and the top being the decimal as far as you have figured it out.

Which doesn't prove that there is a number for anything that can be expressed by a horrendous number of decimals.

The classical greeks understood PI. They also understood the "golden ratio" for a rectangle of same side to side ratio as the remainder after a square has been removed from one end equal to the short side - that ratio is 1/2 +/- [squareroot(5)]/2.

Yes - and they understood that pi and sqrt(5) are no numbers, nor rational proportions, but rather spacial proportions between incommensurables - and that cannot be exactly calculated, only exactly construed by geometric means.

Denying that a number exists does not negate it's existence. The world is not limited by your lack of understanding.

Nor extended by yours.

I can say that "Hans Georg Lundahl doesn't exist" and I am much more likely to be correct, because you could be just another alias for some weirdo that likes to create havoc on the board rather than discuss things rationally.

Discussing things rationally is what I do - but some weirdos like you cause havoc by refusing to understand when perfectly rational arguments are good proof.

Moving to base 12 doesn't accomplish anything 'special' to the calculation. PI in base 12 is just as real as PI in base 10 or even base 2. Why don't you try base 37? OR tell me what the diagonal dimension of a square with side = 1,000,000,000,000 miles is in inches. Take your time... please.

How many feet/yards are there to an English mile?

Seriously: the point with duodecimals is that the logarithmic values can be expressed as falling between this and that duodecimal point - besides it is fun and the calculation hasn't been done, AND every inch, line, point would be expressed in terms of something divisible by 2 and 3, so only few measurings would NOT simplify by dividing both sides of ratio by potencies of 2 or 3.

OK

AbbyLeever wrote:

The point, luddie, of the letters and words is that this is what you are doing with square root and logarithmic numbers issue. You are saying the "word" [squareroot(5)] doesn't exist. It does exist and denial doesn't make it cease to exist. All numbers are constructs, ideas of value, and claiming one doesn't exist is pure denial. But you are used to denial aren't you?

I can prove the sqare root of five doesn't exist arithmetically: 5 is not a square number!

I can construct with a straight edge, ruler and marker (eg classic greek math) a distance that is represented exactly by the golden ratio. Given one dimension I can predict the other every time with this calculation and it will be correct.

I never said it doesn't exist geometrically: there is a square exactly five times as great as the square size one: its side is the diagonal of an oblong with sides 1 and 2.

You cannot give an exact representation of that distance or make any such prediction of the value only because of self imposed limitations - the description is there, just like the rest of the universe is there.

10 = 2 raised to the (x/y) power (and the proper word is power, not "potency" - drugs have "potency")

Prove there is no value of x and y that make this statement false.

12 inches to a foot, 3 feet to a yard, 1760 yards to a mile, get going luddie the diagonal of the 1,000,000,000,000 mile square is? ... take your time, please, take all the time in the world .... the time it takes the world to go all the way around the sun, the time it takes the sun to go all the way around the center of the galaxy, the time it takes the galaxy to move into a new portion of the universe ... if you get my drift ...

ps - you are not OK (and you still need to divide by 5, 7, 11, 13, 17, etc. so no base will fill your needs, ever).

My point exactly: whatever base is used for a system of logarithms, the only rational logarithmic proportions will be those of the powers of the base - or of a square or cubic root of it. Other logarithms are ARITHMETICALLY chimerae - but chimerae that can be approximated.

AbbyLeever wrote:

luddie, luddie, luddie

how many times: saying something isn't true doesn't make it false, it just makes you limited in understanding. the statement "I can prove the square root of five doesn't exist arithmetically: 5 is not a square number!" is not a proof of anything other than a statement of ignorance. further:

IF

I can prove the square root of five doesn't exist arithmetically: 5 is not a square number!

is a TRUE statement THEN

there is a square exactly five times as great as the square size one: its side is the diagonal of an oblong with sides 1 and 2.

is a FALSE statement

IF

there is a square exactly five times as great as the square size one: its side is the diagonal of an oblong with sides 1 and 2.

is a TRUE statement THEN

I can prove the square root of five doesn't exist arithmetically: 5 is not a square number!

is a FALSE statement (and it is, you just proved yourself wrong)

your diagonal is the number for the square root of 5 as much as the numbers 1 and 2 used to create it.

The diagonal in the 1 by 2 rectangle is greater than the 2 side, but smaller than the 2 and the 1 side together - right?

So it is greater than 2 but smaller than 3 in some respect. But it cannot be a number, since there is no number between 2 and 3. It is size. And size as related to another size without there being any least common measure that can be numbered to form both sizes. The sizes are incommensurable. This is a great proof that size - unlike number - is infinitely divisible, non-atomic.

Arithmetic deals in numbers: multiples of one, each defined as one more added (to one or) to another number. They start with 2 and go potentially on ad infinitum without ever reaching infinity actually.

Geometry deals with sizes and size relations: some being ratios with denominator 1 (yard:foot=3:1), and therefore improperly called numbers, some with another denominator (foot:yard=1:3), called fractions, and some that are not ratios but always fall between ratios: to which belong the relations perimeter:diameter (PI), side to diagonal of inter alia square and 1*2 rectangle. Size is infinitely divisible: however small divisions you make, you can always make them smaller. Some properties of numbers are therefore not applicable to all sizes - and some sizes or size realtions are non-numeric, like the interfractional diagonal:side relations or the non-existent relation of exponents a:b when 10 to the ath=2 to the bth. Non-existent, because no power of ten can equal a power of 2 - that would involve a number having two differnt sets of prime factors.

But give me an alternative GEOMETRIC definition of 10log of 2, I will consider if it is at least as real as the misnomer sqrt of 2.

Hans Georg Lundahl
proud to be a luddite

12 inches to a foot, 3 feet to a yard, 1760 yards to a mile, get going luddie the diagonal of the 1,000,000,000,000 mile square is? ... take your time, please, take all the time in the world .... the time it takes the world to go all the way around the sun, the time it takes the sun to go all the way around the center of the galaxy, the time it takes the galaxy to move into a new portion of the universe ... if you get my drift ...

ps - you are not OK (and you still need to divide by 5, 7, 11, 13, 17, etc. so no base will fill your needs, ever).

I will settle for diagonal of a square 1'*1':

1' 4" 11'" 7"" is too small
1' 4" 11'" 8"" is too big

but not by much.

The diagonal has no common measure.

(no measure common to both itself and the side, that is)