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f = ma



The Sun is a powerful man!

If he dies, everybody dies!

                     –   Dersu Uzala


One of my earliest mathematical insights (or realizations) happened one Sunday morning on our way to church.  Actually, I’m not certain that we (my brother Dan and I) were actually heading to church … but I AM certain that it was NEAR the church.

Dan was running (which was nothing unusual) … and I was off to the side, observing.  And it came to me (suddenly and clearly) – that his speed was (simultaneously) dependent upon (both) the length of his stride, and the frequency of his strides.


Simultaneous dual dependency.


There is a (very) large family of algebraic formulae which share this basic pattern.


One that we are all familiar with (those of us who drive a car) is –   d = rt … which says that the distance (d) that we will travel will be a function of two other things: the rate (r) at which we travel, and the time (t) that we spend moving at that rate.  If we go for two hours at 60 miles per hour, we can get somewhere 120 miles away. If we travel for twice as long, we can cover twice that distance. If we average only half the original rate (maybe because we get stuck in rush-hour traffic) then we will cover only half the original distance.


The reason, though, that I chose f = ma (as the title for this essay) … is a little ‘to one side’.


F = ma  says that the force is equal to the mass ‘times’ (that is, ‘multiplied by’) the acceleration.  (which, by the way – is the same thing as saying that the force is simultaneously proportional to both the mass and the acceleration)


But, let’s divide both sides of the equation by ‘m’…

Then we have  f/m = a … or a = f/m.  

This says that the acceleration of a body will be simultaneously (directly) proportional to the force … and (inversely) proportional to the mass.  

Suppose you were to mount a small jet engine (something which will generate a uniform force) to a model railway car and give it a little brick (as a load) to accelerate … then you measure what happens.  Then you do the same thing again, only you double the load. You put two bricks on the car, instead of only one … and you observe what happens. You will find that doubling the mass reduces the acceleration by the same factor [of two].  (this is inverse proportionality.  Direct proportionality is simpler:  If you increase the force by some factor [say, 2 … by using 2 jet engines instead of one] then you will increase the acceleration by that same factor.


I am bothering with these explanations, though, simply because I do not want  these formulae to be meaningless.


In my view (I’m a philosopher really, not a physicist) the statement f = ma is a philosophical assertion … because it says something about the nature of reality.  (the physicist might regard the same expression as a kind of Law … a rule which is always ‘obeyed’ … and also as an explication of how these various components are inter-related)


Anyway, HERE’S what I want to say about this expression [f = ma … or a = f/m]  …

a’ (acceleration) is behavior.  And this behavior is determined by two things – the outside (the ‘environmental’ forces) … and the inside (the mass of the object itself).


I’m interpreting it this way –     a = f/m means that behavior is a function of two things: the outside and the inside.



Here’s the deal:


We do not have to continue being the brats that we have been our whole lives.  


Why do New Zealanders regard the plastic grocery bag to be the (unofficial) ‘national flag’ of their country? / Why is there so much trash along our roads?  Why is there a floating ‘island’ of garbage in the Pacific Ocean [between Oregon and Hawaii] that’s the size of Texas ?


If I do not lovewhatever keeps me alive and/or makes my life better – then how can I claim that I am not a brat?


Do you know the name of the person that made the favorite pair of shoes that you wear?

The clothes that you wear … do you know what the face looks like of the person who made them?

Probably not … but

are we even grateful?


Do we believe so much in the omnipotence of money that our sense of absolute entitlement is merely confirmed by our owning of them?


We would be better off (and closer to the truth) if we would admit that money  (while a legal societal invention) is fundamentally an illusion. The goods that we buy with money have a level of reality which is higher than that of money.  Mmm?


But even if we are completely willing to allow our sense of entitlement to rob us of a grateful heart – with regard to the ‘basics’ –  of food, clothing, and shelter …


what about those things (both inside us and outside us) which keep us alive and ticking

day in and day out?


The sun

Rain (and all water)

The soil … the earth itself

The air (the atmosphere, the delicate membrane surrounding and protecting our planet.  Think about our airless moon!)

The hydrosphere (three quarters of the surface of the earth is water)

The lithosphere (soil and rocks)

The biosphere (that part of the earth which is comprised of living things – plants and animals)


Shall we allow ourselves to feel entitled to all these things as well?


The earth’s crust (the hard, crusty part) is about as thick (proportionally) as is the skin on an apple.

The amount of water comprising our hydrosphere is (proportionally) about as much water as there is on a wet basketball, once you’ve shaken off the excess.



And what about the INSIDE?


Should we imagine that we could even live without –


our heart (and circulatory system)?

brain (and nervous system)?

lungs (respiratory system)?


and the digestive system?

bones (our skeletal system)


skin (the largest, heaviest organ in our body … the integumentary system)?

                       excretory systems?

endocrine system?

lymphatic system?


Shall we take these things for granted as well?


I (just now) found a piece of construction paper

drew a (rather large) circle on it

and listed the various things which are vital

to my life.

[and tacked it to the wall, where I’ll see it every day]


Inside the circle, I wrote : heart, lungs, brain, etc.


outside the circle (and above it) I wrote down things such as:  sun, air, water, soil & rocks, and so on.

Below the circle, I listed things which benefit me which are provided culturally, through the big economy: water systems/delivery; food (production & distribution); shelter, electricity, etc.


I color-coded the entries in order to distinguish between things without which I simply can not survive … and those things for which I am grateful, but which (only) make my life better or easier.  [And I’ll make changes to this little ‘poster’ … as my understanding (or my heart) grows.]


Why did I do this?  [make this little graphic and put it up on my wall]?

Because – I would like to suggest that YOU do it too …  (and nobody likes a hypocrite).


I also think it’s worthwhile – to include these (vital or beneficial) things in routine meditation.

(I do this.)


Also – when I hurt some part of my body (if I stub my toe, for example) then … I apologize to my toe.

It was (though unintentional) my fault, after all.  [It wasn’t the toe’s fault!]  It serves me day in and day out; and I should take care of it.  When I fail to protect it, I should apologize.  (I have done this for many years.)


We should do whatever we can to strengthen a heart connection (love, gratitude) from our own consciousness toward the things which uphold our lives.


If we don’t –

we may be brats our entire lives


and we’ll be more likely to

continue to destroy our only planet-home … (or to allow it to happen)



3 thoughts on “f = ma

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