Prime-Related History: Leibniz' "Universal Language Based on Primes"

[ewmayer]

http://itre.cis.upenn.edu/%7Emyl/lan...es/000729.html

""it takes a really smart person to have a really spectacularly stupid idea" :)

[mfgoode]

Interesting reading and a smart theory of relating sense into numbers, specifically prime numbers. Most lightning calculators do this sort of thing all the time. History narrates that most of these calculators are abnormal and socially inadept in their dealings with others, some were even physical freaks.

Well Mark lieberman has presented a good case history of Liebnitz 'generalis' and ratiocentercalculator but evidently has not considered Kurt Geodels Incompleteness theorem which was the death knell of all such possibilities.

I give below a very elementary version of what Geodel meant by his theorem and struck at the foundation of Peano Arithmetic. Bertrand Russell did the same for Frege's theories of sets.

Browse thru it and lets have your comments.

http://godel.4mg.com/

Mally

[ewmayer]

Originally Posted by ewmayer

""it takes a really smart person to have a really spectacularly stupid idea"

I just came across an earlier versions of the same sentiment expressed in converse form:

"There is no idea so stupid that you can't find a professor who will believe it." -- H. L. Mencken

[m_f_h]

Originally Posted by ewmayer

http://itre.cis.upenn.edu/%7Emyl/lan...es/000729.html

""it takes a really smart person to have a really spectacularly stupid idea" :)

The guy who wrote that article seems to think that 27 is a prime number, so he's quite on the safe side of having a spectacular idea...

I think Leibnitz' idea is a precursor of coding theory; today in computer age we laugh about the simple-mindedness of his concept since we know much about Information theory, compression algorithms like LZH, etc. etc. but at that time (try to figure out how life was when he lived) it's quite bleeding edge thinking. Probably it was before he "invented" the base-2 system for machine calculations (else he might have tought of assigning 2^n to concept #n which gives higher numbers than prime[n] for "primitive concepts", but since one can use addition instead of multiplication one is guaranteed that a "composite concept" is not more than twice its "biggest" ingedient - and it's easy to count the number of primitive concepts involved...)

But well, major drawbacks of course still include
* commutativity of the arithmetic operations which seem not to allow non-commutative chainment of ideas
* the political wars will still continue on the subject of which #n should be attributed to which concept - does communism or capitalism come first ?

[ewmayer]

Originally Posted by m_f_h

The guy who wrote that article seems to think that 27 is a prime number

Sorry, I simply don't see anything that could be construed as such in the article. Liberman may be more cunning linguist than mathematician, but IIRC his academic specialty is computational linguistics, so I'd say he's a little more mathematically savvy than you give him credit for.

But in any event, if you can show me where he writes something that could be reasonably construed as a claim that "27 is prime", I'll be more than willing to change my opinion.

[xilman]

Originally Posted by ewmayer

Sorry, I simply don't see anything that could be construed as such in the article. Liberman may be more cunning linguist than mathematician, but IIRC his academic specialty is computational linguistics, so I'd say he's a little more mathematically savvy than you give him credit for.

Indeed, the memory kinda lingers that your estimation of his abilities is accurate.


Paul

[BlisteringSheep]

I believe that the misunderstanding can be explained through the following:

A casual reading might imply that Mr. Liberman is saying that 27 is prime:

From the 2nd paragraph:

The key ideas were a characteristica universalis that assigns a different prime number to each primitive concept

and from the 4th paragraph:

and we've assigned 27 to the concept "implies"

However, a more careful reading, including

and a calculus ratiocinator that creates complex concepts by multiplication

illuminates that he is instead saying that the "implies" concept is not primitive, but is complex.

Of course, I could really just be experiencing "a bunny with a pancake on his head" moment, and not know at all what I'm talking about....wouldn't be the first time today..

[m_f_h]

Originally Posted by BlisteringSheep

However, a more careful reading, including illuminates that he is instead saying that the "implies" concept is not primitive, but is complex.

Of course I noticed that combination of primitive concepts is possible and corresponds to multiplication of primes. But 27=3*3*3 and I felt justified to exclude the possibility that the concept of "implies" could be reduced to combination of three identical copies of whatsoever primitive concept (the one corresponding to 3).

(Even though I know how any logical operation can be constructed using only NAND gates... and also using only implications, which makes them a good candidate to be chosen as the most primitive logical operation and, as such, as a primitive concept.)

But in any event, if you can show me where he writes something that could be reasonably construed as a claim that "27 is prime", I'll be more than willing to change my opinion.

What I was critisizing is that somebody qualifies several 100 years later "a spectacularly stupid idea" an abstract concept, way ahead of its time, conceived by a not-to-be-proven genious. That's too easy, and in that way one could laugh about the "naiveness" of thinking of almost any genious the world has seen so far.

But in any event, if you can show me where I write something that could be reasonably construed as a claim that "[he] said that 27 is prime", I'll be more than willing to vigurously dement that accusation...

[ewmayer]

Originally Posted by m_f_h

But in any event, if you can show me where I write something that could be reasonably construed as a claim that "[he] said that 27 is prime", I'll be more than willing to vigurously dement that accusation...

Easy:

Originally Posted by m_f_h

The guy who wrote that article seems to think that 27 is a prime number

Also note that "dementieren" is one of those words that one has to be careful when translating into english, because although there is a similar-sounding word in english, it means something rather different. I think you want "deny" or "disclaim" here. (I frequently have the same problem when trying to go back to German from English: e.g. "ordinary" does not translate to "ordinär", at least not with respect to the modern usages of those words. Same problem with eventually != eventuell)

[mfgoode]

Originally Posted by m_f_h

The guy who wrote that article seems to think that 27 is a prime number, so he's quite on the safe side of having a spectacular idea...
?

Well it depends which domains you are considering. How about 4x - 1 ?

Mally

[m_f_h]

Originally Posted by ewmayer

Easy: (...)

I believe that the misunderstanding can be explained through the following:
A casual reading might imply that m_f_h is saying that Mr. Liberman is thinking that 27 is prime.
However, a more careful reading, illuminates that he is instead saying that "the guy seems to think that 27 is prime". Herr Wunderdoktor, darf ich Ihnen eine unverbindliche Gratis-Englisch-Lektion angedeihen lassen:
"seems to" means that "(at a first glance) it appears as if". This is just what has been confirmed by the sheep.

But please: - Although I'm easily stimulated to reply (often in a /seemingly/ aggressive manner) to a provocation, I don't want to be in war with you and herewith make the honest proposal to dig in the Kriegsbeil (up to the next provocation, at least ).

Originally Posted by ewmayer

Also note that "dementieren" is one of those words that one has to be careful when translating into english, because although there is a similar-sounding word in english, it means something rather different. I think you want "deny" or "disclaim" here. (I frequently have the same problem when trying to go back to German from English: e.g. "ordinary" does not translate to "ordinär", at least not with respect to the modern usages of those words. Same problem with eventually != eventuell)

Thanks I know quite well the differences between ordinary and ordinär, eventually and eventuell etc. As to dement, I wasn't too happy with that choice but did not want to use "deny" (makes me think of "access denied") nor "disclaim" (would probably have been better, though).
(I did not want to make allusions to dementia...)