Water, Geometric Progressions, and the iPad (not necessarily in that order)
Posted by John Crutchfield on February 11, 2010
Aloha
Today is the 11th of February 2010. Wow! Amazing 2010 is here and moving on with the speed of a lead-filled luge on a frozen Himalayan hillside…
I love the fact that here we are already one decade into the 21st century and picking up speed and intensity. For many this can be attributed to the geometric progression that is life in general ( o.k. for those not familiar with the term…and I have to say that I mean geometric as exponential expression of life….With exponential growth at a constant rate note that, for each successive period of time, the absolute increase constantly doubles.
The same does not apply to the linear growth model. That is why I feel justified in stating that population doubling “leads to” exponential growth. However, perhaps a better way of expressing this is to say that the nature of exponential growth is more accurately represented by the population doubling series. The nature of linear growth is more accurately represented by a linear series.
e is the key
A key difference between linear growth (simple interest) and exponential growth (compound interest) relates to the number e defined as a limit, which is explored in brief in Simple and Compound Interest and The General Situation (from Answers and Explanations, Mathematics Network, University Of Toronto, Canada (1997).
As described in the Academic Press (Daily Insight) in “Math Buffs Find an Easier e” (1998):
“For both bankers and bugs, e describes a basic limit to exponential growth. For example, if you invested $1 at 100% interest, compounded monthly you would have $2.61 at year’s end. If the interest is compounded every 30 seconds, you would end up with about a dime more. No matter how frequently you earned interest, you would never take home more than e multiplied by the number of dollars you first deposited.”
In short, e effectively defines the difference between linear growth and exponential growth.
The constant of proportionality
One last feature of exponential growth at a constant rate was eloquently summed up by Malthus himself:
“A thousand millions are just as easily doubled every twenty-five years by the power of population as a thousand.”
(I want to thank http://members.optusnet.com.au/exponentialist/Linear_Vs_Exponential.htm for the above explanation)
This can be easily explained: an arithmetic progression can be described as 1+1=2, 2+1=3, 3+1=4 etc.
Whereas a geometric (exponential) progression can be described as 1×1=1, 2×2=4, 3×3=9, 4×4=16, etc.
See how the numbers increase more rapidly per equation in the ones using the ‘x’ vs. the equations using the ‘+’?
That’s what I’m talking about here!
Life being exponential produces resulte which grow rapidly in number and intensity.
This is why Einstein is often quoted as saying that in his estimate the most powerful force in the universe is compound interest (as anyone with a credit card who has a running unpaid balance can testify!)
Anyway, my point was actually to simply remark that things seem to be speeding up and densifying (i.e. more of everything-stuff, people, ideas, info, etc.)
And I like it. “Hang on to your hats, folks, because the ride with most probably increase in speeding up!” According to many scientists, we’ve not gone over the edge of this rollercoaster ride as of yet, but we’re getting closer each moment.
This brings me to a cool thing which I came across this morning….
On Dr. Mercola’s site which, by the way often has some very cool info in addition to a ton of sensible & positive health advice there was a video describing a new gadget by a company based in Sweden known as Bonnier and called a ‘Mag+’.
Check it out here by pasting this link in a new browser window or tab:
http://tinyurl.com/ybhzap7
Come on back here to read more….(if you’re not in a new window there’s always the trusty back button in your browser…)
O.k. there are a few more things to address this morning and the number one thing is H2O.
Yup, that’s right water!
We could talk and write for the next year and still ot cover this most important subject to human life…
But, what I want to do right now is to just begin to scratch the surface of the necessity of water for daily life and specifically to encourage us all to drink a bunch everyday…
How this fits together with the previous posts is that we’re building an toolbox of approaches to life which are intended to result in a higher quality of mental, physical, emotional, (how about financial?) and hopefully spiritual wellbeing.
So I discussed briefly in an earlier post the importance of awareness to learning and improving literally anything…a few of the components of learning being awareness, memory, assesment and choice….
There are tons of books out in the world today describing the importance of water to the basic functioning of the human body my favorite being, “Your Body’s Many Cries For Water” by F. Batmanghelidj, M.D
On his website he says, “Water is the basis of all life and that includes your body. Your muscles that move your body are 75% water; your blood that transport nutrients is 82% water; your lungs that provide your oxygen are 90% water; your brain that is the control center of your body is 76% water; even your bones are 25% water.
Our health is truly dependent on the quality and quantity of the water we drink.”
“ Dr. B’s pioneering work shows that Unintentional Chronic Dehydration (UCD) contributes to and even produces pain and many degenerative diseases that can be prevented and treated by increasing water intake on a regular basis.”
Also, consider this: the human brain is an enormous biochemical electric organ. And we all know that water is a super conductor of electricity (remember not to stand in the bathtub when holding on to an electric cord?)
So there is a growing body of evidence that increasing our water intake can also contribute to more efficient brain functioning (footnote forthcoming.)
So what does all this mean to us and how can we use it today to get more bang for our buck?
Well, basically begin to increase your daily water intake to include an average of 1.5-2 quarts/liters of pure water. That means filtered water, NOT tap water (all due respect for our benevolent government sources and their chlorination/fluoridation actions.) Juice, teas (herbal/caffeinated), coffee, sodas, alcoholic drinks are extra….
2liters H2O/day is the goal….
If all you can afford at the moment is tap water, go for it. However, please be advised that chlorine (added to most, if not all of municipal water souces in USA and many places elsewhere) is a poison designed to killed bacteria, etc. This is a good thing. However, it also kills humans, builds up in the human body and is even nasty for the human skin bonding with the oils of the skin and washing them off (hence the dry skin we feel after showering…heck! I thought it was living in the Los Angeles air that was doing it to me until I got a chlorine shower filter and 3 days after using it never needed lotion again…)
So, point is, find some way to filter the chlorine out of the water you drink…I’ll be happy to do an article in the future on water filters (I don’t sell any at the moment) if anyone’s interested.
Got some thinking to do? Drink a glass of water and watch your thinking clear up a bit. Water enhances the brain activity by facilitating synaptic activity (i.e. the electro-chemical communication process of our brain.)
Need some energy? Drink a glass of water.
Hungry? First drink a glass of water then wait a few minutes before choosing what you want to eat.
Stressed? Drink a glass of water.
Emotionally agitated/disturbed? Drink a glass of water. Take some time to simply breathe and observe your body.
Confused? Drink some water.
To clear here, water is not a panacea/cure-all. However, as the major ingredient of our bodies and a main component to our bodies’ systems’ optional functioning, it’s good to have ‘all hands on deck’ as it were when we want to have a decent chance at creating a happy life.
What I do to encourage myself to drink 2 liters of water each day is to fill up 2-one liter bottles with water and carry them around with me wherever I go. Everytime I have a moment (waiting at a stop light while driving, for example) I pop open the bottle and swallow some water…
I have to say that, originally I was not someone who liked or even thought about drinking water…I’ve gone days in the past without even so much as a passing thought that I was thirsty (maybe even weeks)…So, now knowing what I know, I’ve devised a few strategies to encourage myself to drink more water….
One was to have 4-16oz plastic bottles which I filled with water each day and then set up around me at varioun strategic locations (on the kitchen sink, in the bathroom, on my desk, in the car, even in the middle of the doorway on the floor if I hadn’t been successful in drinking it by any other means) to be consumed before
sleeping….(kind of like target practice and shooting cans off a fence.)
Another has been to commit to taking a drink of water everytime I even so much as think about anything liquid (the clouds, the ocean, rain, rivers, the saliva in my mouth, tears, etc.)
Another was to drink water while I was warming up my car to go somewhere.
As I mentioned above, at the present, I carry 2 glass 1 liter bottles of water wherever I go and evertime I even look at them or touch them, if I can, I take a drink of water.
So, the message for today is that water is our friend!
Thanks for being!
Aloha & Namsate’
Now must go!
Peace
John C. =0)
