Hello Guv.

Hi,

haven't been around for a while but I thought it was time for a bit of mathematical philosophy/history.

Only problem is I can't come up with a question for you. I'll spend the weekend thinking of one.

Cheers,

P.

PaulW: Hello, good to hear from you.

I am seldom too busy for a discussion of history, programming, philosophy, math, physics, infinity, girls, whatever.

BTW: All of my life, I have used math as an abbreviation for mathematics. Recently, I have noticed people using maths. I do not mind typing the extra letter, but I have trouble pronouncing the latter abbreviation.

Is there a rule or law that says an abbreviation must look plural if the word it stands for looks plural?

Naw, it's just an Americanese/English thing. Doesn't really matter, everyone knows what you mean ;)

There's a handy dictionary here for all you English - Americaneese needs.

That's kinda handy, except it seems to think that "masonite" (Americanese) translates to "fiberboard" (English), which is a mispelling if you're English.

PaulW: My knowledge of Math History consists of a lot of disorganized fragments.

I can deliberately remember all sorts of math methods & techniques. For history of math I cannot remember much without something/somebody triggering an association.

I do remember the Babylonians using base 60, resulting in our hours, minutes, seconds for time and 360 degrees per revolution, et cetera. I am pretty sure they used this radix due to its making so many of the common fractions come out even. I do not remember if they had a positional notation with the base 60 equivalent of decimal fraction notation. They might have had something along these lines, but with problems for never ending fractional representations.

I do not remember the Babylonians as being really good at math, but the Greeks were incredible in their knowledge of math and science, if you consider the limitations of their technology. Some Greek estimated the circumference of the earth with an error of 2-4 percent. He based his calculations on the shadow lengths of vertical poles at different latitudes. Another Greek had a not bad concept of matter being made of a small number of atoms (not the earth, water, fire, and air theory). He knew enough about permutations and combinations to realize that less than 100 elements would be sufficient to be the basis for millions of compounds. The Arabs are generally given credit for a lot of math and science, but much of it was rediscovered or copied Greek knowledge.

Maybe we or somebody else can come up with some philosophical (math or other) issues of interest.

There is not much controversy in math aside from issues relating to interpretations of the really esoteric subject matter like infinity, implications of the Godel theorem, discussions of what is provable, et cetera. Perhaps we should try to start a controversy in the Chit Chat Forum.

I have been intending to post about mainstream science never having been wrong, in the sense that everything they ever believed seemed like the best available ideas at the time.

Another controversial but obviously true thought is that the average person owes a lot to the so called robber barons, who are unjustly viewed as villains instead of benefactors.

The post mentioning arithmetic using Roman numerals made me think of a story which may or may not be true.

In ancient (and perhaps medieval) times they had counting houses. Slaves did addition and multiplication by counting huge numbers of pebbles or small rocks or something. This much is true.

The story I wonder about deals with slaves who just made up results without doing the work. After all, how much fun is it to count out 42 piles of rocks with 29 rocks per pile? Then you have to count up to 1218 to determine the product.

The story is that some slaves realized that nobody knew the correct results for the arithmetic, so why not play gin rummy and then make a credible guess? When the plot was discovered or suspected, the masters started using groups of three slaves who were isolated from each other. If all three disagreed, all got beaten. If two agreed, the third got beaten.

Does anybody know how much of the above is true. My father had a sense of humor and often made up strange stories which I often accepted as true. The above might have been one of them. I remember the following are two that I believed until I was 7-10 years old.

I once asked my father why dogs lifted their legs to urinate. He told me that in times long past, people constructed flimsy buildings that easy fell over. The dogs learned to put one leg up to support the wall because they could not run from a falling wall while relieving themselves. Modern dogs were too dumb to know that people no longer made flimsy buildings.

Another about dogs relates to the reason why dogs sniff each other. In this story, a beloved prince from the kingdom of dogs was lost or kidnaped. There was a huge reward for his recovery, like maybe a lifetime supply of all the steak a dog could eat. The missing dog could be recognized due to his s**t smelling like perfume. Hence dogs were always checking for the missing prince of dogs by sniffing.

I read somewhere that the Babylonians reached 60 by counting on their fingers. Up to 5 on the right hand, and then recording the number of fives by holding the thumb of the left hand on successive joints of the left hand fingers. So If your left thumb is on the tip of the first finger, the count is 15 plus the number of extended fingers on the right hand.
Thumb on the ring section of the ring finger = 35 + extended right fingers.
It seems more efficient than stopping at 25 like most of us and you could keep a lot more cows.