Exponential

[martin goddard]

Just a little mathematical aside which might be of interest (or not).


The popular every day use of exponential is to describe a situation in which the rate of growth is curving upwards or accelerating.
This works fine and is widely agreed.

However (here it comes)
I will include some/ enough information to help folks become informed. No need to add extra detail (complex numbers and asymptotes) to impress.

An exponential movement can be  flat, straight,  curving upwards or going curve downwards.

e.g. 6³

3 is the exponent (often called power)

If the exponent is zero the results are a flat line of 1s
If the exponent is one the results are a straight line going up
If the exponent is more than 1, then  the upward and popular curve is created. ie the common usage.
If the exponent less that zero (minus numbers) the curve gets flatter and flatter, dying out toward zero.

This means that "exponential" is an acceptable phrase, but about as precise as "mega", "whopping", "humungous"  or "my word that is large".

That will start the day well for all?


martin

[Leman (Andy)]

This sounds a bit like most wargamers' collections, although very few curve downwards.

[Colonel Kilgore]

Thank you for this post, Martin.

Reading it has improved my day... ... asymptotically (i.e. there is a limit  ).

Simon

[Sean Clark]

I have to say that any use of the exponential  by myself is with regard to the common usage. This explanation though is very interesting.

My own thought for the day.

The word attrition is often used to reflect the wearing down of something through constant conflict with an opposing force and was in fact part of allied policy during the First World War.

However, the etymology of the word links it to the word  contrition (noun) or contrite (adjective).

Attrition is a lesser form of contrition, most often used in religious context meaning to be sorry for your sins, but falling short of full repentance. The verb is attrit meaning to wear down, and actually originates in usage from the First World War as a backwards word construction from the word attrition.

Interesting, eh?

[Colonel Kilgore]

Now that is interesting (too) Sean.

I will in future games concentrate on attritting my opponent 

Simon

[martin goddard]

I am sorry for my sins (sorry) but there are unknown unknowns which I am not knowing?

martin

[Sean Clark]

As Rumsfeld once said, "you don't know what you don't know."

[Colonel Kilgore]

Ah - the Rumsfeldian branch of mathematical mysticism...

Simon

[Smoking gun]

The trouble with higher mathematics is that numbers just don't add up.

Best wishes,
Martin Buck

[steve_holmes_11]

Exponential growth really means is the exponent is increasing in the function.
Not the base number as in the intial examples.

The term is  badly abused in news reporting (see also "decimated").

[Colonel Kilgore]

Steve,

"Decimated" bugs me too - whatever happened to a decent classical education?! 

Although I did see recently that the dictionary-accepted use of the word now includes the meaning as the press has it. A sad day for numerate Romans...

Simon

[Bankinista]

It's the same sort of thing with vehicles. Anything with tracks is a tank.

Bankinista

[Colonel Kilgore]

I think anything with armour, even if it has wheels, can be a tank!

Simon

[Sean Clark]

There is a growing tendency to accept that language usage evolves over time and that words can be appropriated for meanings other than their original definition. The Oxford dictionary reveals 'new' words'  most years that are included in updated editions. 'Chav' is one word that comes to mind. Due to its usage in the common vernacular, it now exists as a word in the OED. Quite whether I'm ready to accept it on the Scrabble board yet, I'm not so sure! 

I'll definitely use 'Exponential', especially if it's a triple word score 

[Leman (Andy)]

Having watched Fall of the Roman Empire in my youth, which featured an actual decimation, with every 10th man being pushed off a wall atop a cliff, as a punishment for the whole unit, and also having to struggle through Latin O Level, it does bug me when the word is used so very incorrectly. Only this morning I watched an American Battlefields Trust short on Custer's Last Stand Hill in which the 7th Cavalry were described as being decimated at the Little Bighorn. If only .......... they would have returned from the battle having suffered only 50 or so casualties! Maths may have been wasted on me at school, but not Latin.