**I wrote:**

^{10}log of 2, because no potency of two exactly equals a potency of 10, just as there is no arithmetical sqrt(2), because 2 is not a sq #.

^{10}log of 2 is, in so far as in any sense it is. Rather, I see it more clearly.

^{10}logs anew, but in fractions expressed in duodecimal fractions rather than in decimals. But it is a pretty hard work to figure out the ninth root of ten (cubic root of cubic root) and put it in the fourth potency (square of square) just to get at the value for

^{10}log : 4/9.

A few days ago, I started anew.

- 1' (foot)=12" (inches)
- 1"=12'" (lines)
- 1'"=12 "" (points)
- 1'=12"=144'"=1728""

^{10}log of 2.

- 144:10=14 2/5
- 14 2/5*3=42 6/5=43 1/5

^{10}log of 2.

^{th}potency of ten - 100,000,000,000 - is greater than the 36

^{th}potency of 2 - 68,719,426,736 - so 44'" is upper limit for

**10log of 2**in the first approximation.

^{d}potency of a number, you multiply the logarithm with two, according to general rule that adding logarithms means multiplying corresponding numbers.

**(=10log of 2*2) would thus be between 86'" and 88'". 87'" come in between. 87:144=29:48. Is that more or less than the 10log of 4?**

^{10}log of four^{10}log of 4, so the half must be reduced from 44'" to 43'" 6"" as upper limit for

^{10}log of 2.

**, subtract 10log of 2 from 1 (=**

^{10}log of 5^{10}log of 10). To get that

**of 25**, add it to itself. To get that

**of 2.5**subtract 1' from

^{10}log of 25. Add

^{10}log of 5 and subtract another 1', and you have the

**- and when it comes to the**

^{10}log of 1.25**I jumped straight onto the**

^{10}log of 3**: 10**

^{10}log of 9^{20}is less than 9

^{21}, but 10

^{21}is more than 9

^{22}. So the

^{10}log of 9 must be between 20:21 and 21:22. If it is expressed in duodecimals it is easier to halve to get the

^{10}log of 3.

*My results so far:*

^{10}log of 2< 0' 3" 7'" 6""

^{10}log of 4< 0' 7" 3'"

^{10}log of 8

^{10}log of 5< 0' 8" 5'"

**of 25**

< 1' 4" 10'"

**of 1.25**

< 0' 1" 3'"

^{10}log of 9< 0' 11" 5'" 5""5/11

**and of 3**

< 0' 5" 8'" 8""8/11

*Always presuming that 1=1'.*Now for a theoretical definition:

- a
**logarithm is**not a number, but**EITHER a ratio between**the (whole number!)**potencies of two numbers, the base and the number whose logarithm it is**, so that **if**base^{a}=number^{b}**then**the logarithm is a:b**OR**a**geometric irrational proportion**that can only be approximated to above- and furthermore expressed in either case as fractions of an arbitrary length unit, so as to compare with real or virtual counting slides (is that what you call them?) the potencies of numbers, so that multiplication of numbers can by succesful fiction be expressed as addition of potencies and divison by subtraction, potencies by multiplication, roots by division.

No need to dub logarithms numbers in order to understand them, then!*Hans Georg Lundahl*

Continued:The fact that there is no such a thing as a ^{10}log of two is also proven by the fact, that the closer approximations to its value - the LESS they have of the definition of logarithm, i e ratio between exponents of EQUAL potencies.

In order to prove this, consider that 87:288=29:96 is a closer upper limit than 44:144=88:288=11:36.

Now, will the potencies 10^{29} and 2^{96} be more or less equal to each other, than 10^{11} and 2^{36}?

Two^{96} is

79,228 quadrillions

162,514 trillions

55,647 billions

658,951 millions

950,336,

which is more than 20 quadrillions off the 100,000 quadrllions that form the potency 10^{29}.

Clearly this difference is greater than not just the difference between 10^{11} and 2^{36}, but even greater than any of the number involved in that real inequality and nearest possible equality.

Oh, yes - when I had taken the sweet trouble (like a crosswordpuzzle) of calculating 2^{96} in a few grid systems, I found it quite as worthwile to go up a few potencies of two by doubling.

31:103 is a closer lower limit (closer than 3:10), because

10 quintillions

141,204 quadrillions

801,799 trillions

122,900 billions

345,849 millions

643,008

is greater than 10 quintillions.And the upper limit can be drawn down to 32:106.

The new approximations are:

0' 3" 7'" 4""8/103

0' 3" 7'" 5""35/53

Which I found out in proving that what is thus approximated can be infinitely approximated and never reached because it doesn't exist.

HGL**Résumé of mathematic debates with Voice Of Principle:**

- a) He attacks my argument against the regress to infinity "infinity cannot be passed through" as having been refuted by modern mathematical understanding of infinity, also he attacks my logic on logic thread by claiming there is reason that goes counter to logic and is still true
- b) I answer that every number is finite, a multiple of one, and that every number is rational
- c) He counters with saying that Greek math's thought so, but PI and sqrt/2, being irrational, disprove this
- d) I answer that I know very well that PI and "sqrt/2" are irrational, it is the number part of their categorisation I disagree with, since they aren't numbers but size relations
- e) message disappears
- f) when I repeat the point, VoP claims my limited understanding of number cuts me off from understanding the great new "discoveries" of math's since Newton
- g) On a thread on geocentrism/heliocentrism, Rita claims the main argument for heliocentrism is that Copernican hypothesis of Universe makes accurate calculations of planetary movements possible
- h) I counter saying that mathematic fictions can make calculations easier without being true to mathematic realities and give as example the fictitious negative rule of squares (a - b)sq = asq - 2ab + bsq, proving this is geometrical nonsense if taken to the letter, step by step, as contrasted with real rule (a - b)sq = asq - bsq - 2b(a - b), which is true to geometry, involves no supposition of negative numbers existing, but is less handy
- i) VoP claims I misrepresent algebra and claims it doesn't involve any fiction, repeating that my limited understanding of mathematics cuts me off from many great discoveries
- j) I disprove both his points by this thread, calculating the
^{10}logarithms of 2, 3, 4, 5, 8, 9, 25 and 1.25, especially refining the logarithm of 2, while saying that it is not a number and what it really is: a relation, and, since exponents must be whole numbers, a fictitious relation between exponents of 10 and 2 when their powers equal - which Eratesthenes has proved they never do. To substantiate my claim of calculating the log of 2, I show my calculations in part and give the values in duodecimal fractions, corresponding best both to my old dream of making counting slides on a yardstick and to my calculations - and leave it to VoP to convert the duodecimals into decimals to check my accuracy - k) VoP does not answer, but AbbyLeever, who has not followed my debates does, repeating VoP's misundestanding of my arguments.If he had been a zen buddhist, I think he might have understood my mathematics better - not that that would have saved his soul of course, but it would have been more stimulating on this board.

*Hans Georg Lundahl*

## 4 comments:

1 ...on classical Greek mathematics, or logarithms f...

2 ...to AbbyLeever on my classical Greek logarithms

3 AT LONG LAST, VOP!

4 lighting up dialogue with myshkin and finishing it...

retrieved from:

http://www.webcitation.org/5cRam7jOD

See also later two messages, starting with:

... on reality of existence of numbers (and on Pythagoreans and Bruno)

See also, on another blog:

Quote from Aristotle

Two more than two make four - but why?

What are Franctions?

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