Force on charges stacked in evenly spaced series at a single moment in time

 

Net force on point charges stacked in evenly spaced series at a single moment in time

It is at a single moment in time when all of the charges would be an equal distance from the next nearest charge as measured in a single dimension after that point of time some of the charges might move to a new position

In a one dimensional tube uncharged tube of length L going from left to right

The distance between the two farthest point charges from each other is L

N is an integer greater than or equal to two equal to the number of point charges

The total charge of all point charges is N

The charge of each point charge is Q/N

The distance between each point charge and the nearest point charge is D

D = L / ( N -1 )

Fi is the Individual force a point charge on the farthest right experiences from another point charge listed with an index of i where the charge farthest on the left has i = 0 the charge second farthest to the right has i = n - 2

Fi = [ L - i * L / ( n - 1 ) ] ^ 2

F = sum of all Fi from i = 0 to i = n - 2

Incomplete next steps

Look up notation I used in place of standard calculus symbols when letters and numbers and askey symbols are used instead of hand drawings from previous articles

Take limit as n approaches infinity to calculate F for a unlimmitted number of point charges using an integral

Compare that for all other variables having the same value but n equalling two

Do in two and then three dimensions next for the point charge in a single corner

Note :  trig functions might be useable to estimate distance between charge as a function of angle but might give wrong results if used as an integral of force with respect to angle from one angle to another angle to calculate net total force experienced by a charge in a corner of a square or cube, so it is probably better to use indexes i, j and k and do double or triple integral using caartesian coordinates instead of single or double integral using polar or spherical coordinates because the number of point charges in each angular direction maybe different 

Copyright Carl Janssen 2022 Jan 12

Tangent of the average of two angles and other trigonometric identities derived from a combination of it and the pythagorean theoreom

Tangent of the average of two angles and other trigonometric identities derived from a combination of it and the pythagorean theoreom

The tangent converts an angle into a slope

Take two points in polar coordinates of (1, A) and (1, B) on the unit circle

convert those points into caartesian coordinates and get (cosA, sinA) and (cosB, sinB)

A midpoint that is the average of their caartesian coordinates exists in between those two points having coordinates of 

( 0.5*cos(A)+0.5*cos(B) , 0.5*sin(A) + 0.5*sin(B) ) caartesian

It has a radius in polar coordinates of

( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5

The midpoints angle in polar coordinates must be the average of the polar coordinates' angles of the two points it is in between in this specific case.  The midpoint of any two polar coordinates with the same radius away from a common origin ( pole 0 ) is located at the average of their angles but maybe with a different radius when expressed in polar coordinates.

This midpoint is located at

( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5, (A+B)/2 )    polar 

the slope from

 (0,0) to the midpoint 

(0,0) to (0.5*cos(A)+0.5*cos(B) , 0.5*sin(A) + 0.5*sin(B) ) caartesian

(0,0) to ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5, (A+B)/2 )    polar  

Is the same as the slope from (0,0) to a point on the unit circle with the same angle in polar coordinates as the midpoint

(0,0) to ( 1, (A+B)/2 ) in polar coordinates

N = 1 / ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5

The point on the unit circle (1, (A+B)/2 ) polar 

is the same as

( N*[0.5*cos(A)+0.5*cos(B)],  N*[0.5*sin(A) + 0.5*sin(B)] ) caartesian

Since that point is on the unit circle the following is therefore true

cos([A+B]/2) = N*[0.5*cos(A)+0.5*cos(B)] =

= [0.5*cos(A)+0.5*cos(B)] / ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5

sin([A+B]/2) = N*[0.5*sin(A)+0.5*sin(B)] =

= [0.5*sin(A)+0.5*sin(B)] / ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5

Since the tangent is the slope of an angle the following is therefore true

tan([A+B]/2) = N*[0.5*sin(A) + 0.5*sin(B)] / (N*[0.5*cos(A)+0.5*cos(B)])

tan([A+B]/2) = [0.5*sin(A) + 0.5*sin(B)] / [0.5*cos(A)+0.5*cos(B)]

tan([A+B]/2) = [sin(A) + sin(B)] / [cos(A) + cos(B)]

The following simplifications can be made for half and double angle trigonometric values

sin(0) = 0

cos(0) = 1

tan([A+0]/2) = [sin(A) + sin(0)] / [cos(A)+0.5*cos(0)]

tan(A/2) = sin(A) / [ 1 + cos(A) ]

[tan(A/2)]^2 = [ sin(A) ] ^ 2 / [ 1 + cos(A) ] ) ^2

[sin(theta)]^2 = 1 - [cos(theta)]^2 = [1-cos(theta)]*[1+cos(theta)] 

[ sin(A) ] ^ 2 / [ 1 + cos(A) ] ) ^2 = [1-cos(A)]*[1+cos(A)] / [1+cos(A)]^2

[ sin(A) ] ^2 / [ 1 + cos(A) ] ) ^2 = [1-cos(A)] / [1+cos(A)]

[tan(A/2)]^2 = [1-cos(A)] / [1+cos(A)]

tangent of half angle confirmed 

https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities#Half-angle_formulae

let x = cos(A/2) and solve using quadratic equation

(1 - [cos(A/2)]^2 ) / [cos(A/2)]^2 = [1-cos(A)] / [1+cos(A)]

( 1 - x^2 ) / x^2 = [1-cos(A)] / [1+cos(A)]

1 - x ^2 = ( x^2 ) *  [1-cos(A)] / [1+cos(A)]

0 = ( x ^2 ) + ( x^2 ) * [1-cos(A)] / [1+cos(A)] - 1

0 = ( x ^2 ) * [1 + cos(A) + 1 - cos(A)] / [1+cos(A)]   - 1

0 =  ( x ^2 ) * 2 / [1+cos(A)]   - 1

a = 2 / 1 + cos(A) , b = 0 , c = -1

x= [ - b +- ( b^2 - 4*a*c) ] / ( 2 *a )

x = [- 0 +- ( 0 - 4 * 2 /  [ 1 + cos(A)] * -1) ^ 0.5 ] / 2 * [2 / 1 + cos(A)]

x = +- ( 8 / [1 + cos(A)] ^ 0.5 ) /  ( 4 / [ 1 + cos(A) ] )

cos(A/2) =  +- ( 8 ^ 0.5 ) * ( 1 / [ 1 + cos(A) ] ^ - 0.5 ) / 4

8 ^ 0.5 = 2 * 2 ^ 0.5

4 = 2 * 2 ^ 1

(8^0.5) / 4 = 2 ^ -0.5

cos(A/2) = +- ( [ 1 + cos(A) ] ^ 0.5 ) / ( 2 ^ 0.5)

[ sin(A/2) ] ^ 2 =  1 - [ cos (A/2) ] ^2

[ sin(A/2) ] ^ 2 = 1 - [ 1 + cos(A) ] / 2 = 0.5 - 0.5 * cos(A) = [ 1 - cos(A) ] / 2

sin(A/2) =  +- ( [ 1 - cos(A) ] / 2 ) ^ 0.5

confirmed

https://web.archive.org/web/20210912185657/https://www.intmath.com/analytic-trigonometry/4-half-angle-formulas.php

N = 1 / ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5

when B = 0  then N = 1 / ( [ 0.5*cos(A)+0.5*1  ] ^ 2+ [ 0.5*sin(A) + 0.5*0 ] ^ 2) ^ 0.5

( [ 0.5*cos(A)+0.5*1  ] ^ 2+ [ 0.5*sin(A) + 0.5*0 ] ^ 2) = 0.25 * ( [1 + cos(A) ] ^ 2 + [ sin(A) ] ^2 )

( [1 + cos(A) ] ^ 2 + [ sin(A) ] ^2 ) = [ cos(A) ] ^ 2 + [ sin(A) ] ^ 2 + 2 * [ cos(A) ] + 1

( [1 + cos(A) ] ^ 2 + [ sin(A) ] ^2 ) = 2 + 2 * cos(A)

 ( [ 0.5*cos(A)+0.5*1  ] ^ 2+ [ 0.5*sin(A) + 0.5*0 ] ^ 2) = 0.5 + 0.5 * cos(A) 

cos(A/2) = [ 0.5*cos(A) + 0.5*1 ] / ( [ 0.5*cos(A)+0.5*1  ] ^ 2+ [ 0.5*sin(A) + 0.5*0 ] ^ 2) ^ 0.5  

[ cos(A/2) ] ^ 2 =  ( [ 0.5*cos(A) + 0.5* ] ^ 2 ) / [ 0.5 + 0.5 * cos(A) ]

[ cos(A/2) ] ^ 2 = 0.5 + 0.5 * cos(A) = [ 1 + cos(A) ] / 2

cos(A/2) =  +- ( [ 1 + cos(A) ] ^ 0.5 ) / ( 2 ^ 0.5)

[ cos(A/2) ] ^ 2 = [ 1 + cos(A) ] / 2

[ cos(A) ] ^ 2 = [ 1 + cos( 2 * A ) ] / 2

cos( 2 * A ) = ( 2 * [ cos(A) ] ^ 2 ) - 1 

confirmed

https://web.archive.org/web/20210421123600/https://www.intmath.com/analytic-trigonometry/3-double-angle-formulas.php

cos([A+B]/2) = [ 0.5*cos(A)+0.5*cos(B) ] / ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ^ 0.5

cos(A+B) = ( 2 * [ cos( [A+B] / 2) ] ^ 2 ) - 1

cos(A+B) = [ 2 * ( [ 0.5*cos(A)+0.5*cos(B) ] ^ 2 ) / ( [ 0.5*cos(A)+0.5*cos(B)  ] ^ 2+ [ 0.5*sin(A) + 0.5*sin(B) ] ^ 2) ] - 1

[ tan(A/2) ] ^ 2 = [ ( sin(A) ] ^ 2 / [ 1 + cos(A) ] ) ^2

[ tan(A) ] ^ 2 = [ ( sin( 2*A ) ] ^2 / [ 1 + cos( 2*A) ] ) ^2

[ sin( 2*A ) ] ^ 2 = [ tan(A) ] ^2 * [ 1 + cos( 2*A) ] ) ^2

[ sin( 2*A) ] ^ 2 = [ tan(A) ] ^ 2 * ( 1 + [ ( 2 * [ cos(A) ] ^ 2 ) - 1 ] ) ^2

[ sin( 2*A) ] ^ 2 = 4 * [ tan(A) ] ^ 2 * [cos(A)] ^ 4 

[ sin( 2*A) ] ^ 2=  4 * [ sin (A) ] ^ 2 * [ cos(A) ] ^ 2 

sin( 2 * A) = 2 * [ sin (A) ] * [ cos (A) ]

confirmed

https://web.archive.org/web/20210421123600/https://www.intmath.com/analytic-trigonometry/3-double-angle-formulas.php

sin(A/2) = [ 0.5 * sin(A) + 0.5*0 ] / ( [ 0.5*cos(A)+0.5*1  ] ^ 2+ [ 0.5*sin(A) + 0.5*0 ] ^ 2) ^ 0.5 

[ sin(A/2) ] ^ 2 =  ( [ 0.5 * sin(A) ] ^2 )  /  0.5 + 0.5 * cos(A) 

[ sin(A/2) ] ^ 2 = 0.5 * ( [ sin(A) ] ^2 ) / [ ( 1 + cos((A) ]

[ sin(theta) ] ^ 2 = 1 - [ cos(theta) ] ^ 2 = [ 1 - cos(theta) ] * [ 1 + cos(theta) ]

[ sin(A/2) ] ^ 2 = 0.5 *  [ 1 - cos(A/2) ]

sin(A/2) =  +- ( [ 1 - cos(A) ] / 2 ) ^ 0.5

[ cos(theta) ] ^ 2 = 1 - [ sin(theta) ] ^ 2

1 = ( 1 / [ cos(theta) ] ^ 2 ) - [ tan(theta) ] ^2

1 + [ tan(theta) ] ^2 = [ cos(theta) ] ^ -2

[ cos(theta) ] ^ 2 = 1 / (1 + [ tan(theta) ] ^2)

cos(theta) = +- 1 / (1 + [ tan(theta) ] ^2) ^ 0.5

[ sin(theta) ] ^ 2 = [ tan(theta) ] ^ 2 * [ cos(theta) ] ^2

[ sin(theta) ] ^ 2 = ( [ tan(theta) ] ^ 2 ) / (1 + [ tan(theta) ] ^2)

cos( [A+B] / 2 ) = +- 1 / ( 1 + [ tan( [A+B] / 2 ) ] ^2) ^ 0.5

cos( [A+B] / 2 ) = +- 1 / ( 1 + ( [ sin(A) + sin(B) ] / [ cos(A) + cos(B) ] ) ^2) ^ 0.5

[ sin( [A+B] / 2 ) ] ^ 2 =  [ tan( [A+B] / 2 ) ] * cos( [A+B] / 2 ) 

sin( [A+B] / 2 ) = +- ( [ sin(A) + sin(B) ] / [ cos(A) + cos(B) ] ) / ( 1 + ( [ sin(A) + sin(B) ] / [ cos(A) + cos(B) ] ) ^2) ^ 0.5

Using sin, cos and tan functions to calculate each other

[tan(theta)]^2 = [sin(theta)/cos(theta)]^2

[sin(theta)/cos(theta)]^2 = (1 - [cos(theta)]^2 ) / [cos(theta)]^2

[tan(theta)]^2 = (1 - [cos(theta)]^2 ) / [cos(theta)]^2

[tan(theta)]^2 = [sin(theta)]^2 / (1 - [sin(theta)]^2 )

Nothing in high school or college geometry is used to do this that has not been taught in prerequisite classes for high school or college geometry other than the definition of trigonometric functions the pythagorean theoreom and converting polar to caartesian coordinates or caartesian to polar coordinates all of which can be taught without prerequisite knowledge from high school or college geometry.  See my essay on why high school or college geometry should be removed and students should go straight to trigonometry without it which explains the cult like nature of high school or college geometry class.

http://teachingthenarrowway.blogspot.com/2021/12/why-you-should-be-able-to-skip-high.html

http://web.archive.org/web/*/http://teachingthenarrowway.blogspot.com/2021/12/why-you-should-be-able-to-skip-high.html

Copyright Carl Janssen 2022

Incomplete work on the following

work on half and double angles, added angles and average angles for functions other than tan(0.5A + 0.5B)

I originally planned to get half an double angles for each trigonometric identity in terms of itself then planned to compare with results published elsewhere but apparently that is not commonly put that way in a table.  Such as for example 

sin of half an angle as a function of sin of a whole angle

cos of half an angle as a function of cos of a whole angle

tan of half an angle as a function of tan of a whole angle

"Each trigonometric function in terms of each of the other five" is not for half and double angles 

https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities

http://web.archive.org/web/20211227144328/https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities

average with respect to time vs with respect to distance

mean average with respect to time vs with respect to distance

Notation

I am writing 2*(1second)^2 with a shorthand of 2 second ^ 2 that is why I am writing meter not meters and second not seconds.  I am doing this because it became very confusing writing out the units differently for plural and singular form such as 2 seconds but 1 second when the units were put to powers other than 1.

x = displacement

t = time

m = mass

f = force

a = acceleration

v = velocity

P = momentum

KE = Kinetic Energy

Int[y, g(y)] = the anti derivative of g(y) with respect to y

dg(y)/dy = the derivative of g(y) with respect to y

Dyg(y) = the derivative of g(y) with respect to y

Example 1

given x(t=0 seconds) = 0 meter

given v(t=0 seconds) = 0 meter second ^ -1

given a(t) = 1 meter second ^ -2

v(t) = t*(1 meter second ^ -2)

x(t) = 0.5 meter second ^ -2 * t^2

t^2 = x / (0.5 meters * seconds ^ -2 ) 

t^2 =  2*x / ( 1 meter per second ^ 2 )

t^2'= (2 meter^-1 second ^2) * x

t(x) = (2^0.5)*(1 meter ^ -0.5 second ^ 1) *(x^0.5)

v(x) = t(x) * (1 meter second ^ -2)

v(x) = (2^0.5)*(1 meter ^ -0.5 second ^ 1) *(x^0.5) * (1 meter second ^ -2)

v(x) = (2^0.5)*(1 meter ^ 0.5 second ^ -1) *(x^0.5)

antiderivative of v(x) with respect to x shall be called Int[x, v(x)]

Dx(x^N) = N*x^(N-1)

Int(x, x^N) = (1/[N+1])*x^(N+1) + K0

Dx(1/[N+1])*x^(N+1) = (N+1)/(N+1)*x^(N+1-1)

Int[x, v(x)] = (1/1.5)*(x^1.5)*(2^0.5)*(1 meter ^ 0.5 second ^ -1) + K1

Int[x, v(x)] = (2/3)*(x^1.5)*(2^0.5)*(1 meter ^ 0.5 second ^ -1) + K1

Int[x, v(x)] = (x^1.5)*(2^1.5)*(1 meter ^ 0.5 second ^ -1) / 3 + K1

x(t) = 0.5 meter second ^ -2 * t^2

x (1 second) = 0.5 meter second ^ -2 * (1 second) ^ 2 = 0.5 meter

Int[x, v(x= 0.5 meter)] = (0.5 meter^1.5)*(2^1.5)*(1 meter ^ 0.5 second ^ -1) / 3 + K1

0.5 ^ 1.5 * 2 ^ 1.5 = 1

Int[x, v(x=0.5 meter)] = ( 1 meter ^2 second ^ -1 ) / 3 + K1

Int[x, v(x=0 meter)] = ( 0 meter ^2 second ^ -1 ) / 3 + K1

Average velocity with respect to displacement from a displacement of 0 meters to a position of 0.5 meter =

= ( Int[x, v(x= 0.5 meter)] - Int[x, v(x=0 meter)] ) / ( 0.5 meter - 0 meter) =

= ( 1 meter ^ 2 / 3 ) / 0.5 meter =

= 2 meter / 3

antiderivative of v(t) with respect to t shall be called Int[t, v(t)]

v(t) = t*(1 meter second ^ -2)

Int[t, v(t)] = 0.5 meter second ^ -2 * t^2 + K2

Int[t, v(t=1 second) = 0.5 meter second ^ -2 * (1 second )^2 + K2

Int[t, v(t=1 second) = 0.5 meter + K2

Int[t, v(t=0 second) = 0 meter + K2

Average velocity with respect to time from a time of 0 second to a time of 0.5 second =

= ( Int[x, v(t= 1 second)] - Int[x, v(t=0 second)] ) / ( 1 second - 0 second) =

= (0.5 meter-0meter) / (1 second-0second) = 0.5 meter second ^ -1

given mass = 1 kilogram

KE(x) = 0.5 * 1 kilogram * [v(x)]^2

v(x) = (2^0.5)*(1 meter ^ 0.5 second ^ -1) *(x^0.5)

KE(x) = 1 kilogram meter second ^ -2 * x

F(x) = dKE/dx = 1 Kilogram meter second ^ -2

P(t) = 1 kilogram * v(t)

v(t) = t*(1 meter second ^ -2)

P(t) = t*(1 kilogram meter second ^ -2)

F(t) = dP(t)/dt = 1 kilogram meter second ^ -2

The average velocity with respect to time is not the same as the average velocity with respect to displacement for an object that starts stationary and experiences constant acceleration when averaged over a distance interval that is the same distance as it would have traveled in the time interval in which it's average velocity with respect to time is calculated.  However the average force it would experience over such an interval would be the same if either averaged by time or by displacement because the force is the same constant amount in either case.  Such would hold true for a falling object experiencing a constant force having displacement, time and velocity measured as zero at the initial starting condition of the fall.

Example 2

given a(t) = t^2 * 1 meter second ^ -4

given v(t=0 second) = 0 meter second ^ -1

given m = 1 kilogram

given x(t=0 second) = 0 meter

v(t) = 4*t^3 * 1 meter second ^ -4

x(t) = 12*t^4* 1 meter second ^ -4

[t(x)] ^ 4 = x / 12 meter second ^ -4

[t(x)] ^ 4 = x*(1/12)*1 meter ^ -1 second ^ 4

t(x) = x^(0.25) * (1/12)^0.25 * 1 meter^-0.25 second ^1

v(x) = 4 * 1 meter second ^ -4 * [t(x)]^3

v(x) = 4*1 meter second^-4*[x^(0.25)*(1/12)^0.25*1 meter^-0.25 second ^1]^3

v(x) = 4 * (1/12)^0.75 * x^0.75 * 1 meter ^0.25 second ^ -1

KE(x) = 0.5 * 1 kilogram * [v(x)]^2

KE(x) = 8*(1/12)^1.5*x^1.5*1 kilogram meter ^0.5 second ^ -2

Dx(x^1.5) = 1.5*x^0.5

dKE(x)/dx = 12*(1/12)^1.5*x^0.5*1 kilogram meter ^0.5 second ^ -2

f(x) = dKE(x)/dx

int[x, f(x)] = KE(x) + K1

x(t) = 12*t^4* 1 meter second ^ -4

x(t = 1 second) = 12 meter second ^ -4 * (1 second)^4 = 12 meter

KE(x) = 8*(1/12)^1.5*x^1.5*1 kilogram meter ^0.5 second ^ -2

(1/12)^1.5*12^1.5=1

KE(x = 12 meter) = 8*1 Kilogram meter ^2 second ^ -2

v(t) = 4*t^3 * 1 meter second ^ -4

KE(t = 1 second) = 0.5 * 1 kilogram * [4 meter second ^ -1] ^ 2

KE(t = 1 second) = 8 kilogram meter ^ 2 second ^ -2

average force with respect to displacement from 0 meter to 12 meter =

=(int[x, f(x = 12 meter)] - int[x, f(x = 0)])/(12 meter - 0 meter) =

= 8 kilogram meter ^ 2 second ^ -2 / 12 meter =

= (2/3) * 1 kilogram meter second ^ -2

v(t) = 4 * t^3 * 1 meter second ^ -4

P(t) = 1 Kilogram * v(t)

P(t) = 4 * t^3 * 1 Kilogram meter second ^ -4

P(t = 1 second) = 4 * (1 second)^3 * 1 Kilogram meter second ^ -4

P(t = 1 second)  = 4 kilogram meter second ^ -1

f(t) = dP(t)/dt = 12 * t^2 * 1 Kilogram meter second ^ -4

int[t, P(t)] = P(t) + K2

average force with respect to time from 0 second to 1 second =

=(int[t, f(t= 1 second)] - int[t, f(t = 0)])/(1 second - 0 second) =

=  4 kilogram meter second ^ -1 / 1 second =

=  4 kilogram meter second ^ -2

f(x) = 12*(1/12)^1.5*x^0.5*1 kilogram meter ^0.5 second ^ -2

f(x=12meter)=12*(1/12)^1.5*(12meter)^0.5 *1kilogram meter ^0.5 second ^ -2

12*(1/12)^0.5*12^0.5=12

f(x = 12meter) = 12 kilogram meter ^ 2 second ^ -2

f(t) = dP(t)/dt = 12 * t^2 * 1 Kilogram meter second ^ -4

f(t = 1 second) = 12 kilogram meter second ^ -2

In this example the instantaneous force as a function of time is equal to the instantaneous force as a function of displacement at the displacement value that would occur for a given time value.  But the average force as a function of time is not the same as the average force as a function of displacement for the displacement interval that matches with the time interval.

Copyright Carl Janssen 2021 December 16

Estimating the gas laws based on collissions

Estimating the gas laws based on collissions

Starting with a simple one dimensional force calculation problem 

An object is traveling back and forth between two walls at a constant speed called travel speed except during collissions.  During collissions the object slows down to 0 then speeds up to it's original speed but in the opposite direction. The walls are parrellel to each other and a distance called travel length apart except during collissions where the wall hit by the object temporarily deforms then returns to it's original shape or is temporarily displaced then returns to it's original position after each collission ends.  The object moves in a path perpendicular to the walls.  The time the object is not in a collission is called travel time and the time the object is in a collission is called collision time.  The length a wall is temporarily displaced in the direction parrelel to the objects path of travel during a collission is called collission length.  The wall is moved or deformed during collission and the object is treated like a point mass with no deformation to make the math simpler.  

Mass refers to the mass of the object in one dimensional force calculations below.  Force below refers to a scalar being the absolute value of the force vectors magnitude and not to the direction of the force vector.  That is I am not counting forces going in opposite directions as having opposite values in the calculations below.  If forces were treated as vectors and no absolute value was taken there would be a zero average force when an equal number of complete collissions in each opposite direction occured.

The mean force the object would experience with respect to time using impulse = change in momentum = force * time

The absolute value of the change in momentum in a single collission is twice the absolute value of the objects momentum in this case because it switches to the same momentum in the opposite direction.

mean force with respect to time during travel = 0

mean force with respect to time during collission = 

= 2*mass*(travel speed) / (collission time)

mean force with respect to time = 

= 2*mass*(travel speed) / ([travel time] + [collission time])

(travel time) = (travel length) / (travel speed)

limit of mean force with respect to time as [(collision time) / (travel time)] approaches 0 is =

= 2*mass*(travel speed) / (travel time) = 

= 2*mass*([travel speed]^2) / (travel length)

The mean force the object would experience with respect to distance using work = force * distance

Work occurs during a collission to slow the object down to zero speed then again a second time to return it to original speed.  So the work done in a single collission is twice the traveling kinetic energy of the object in this case.

mean force with respect to distance during travel = 0

mean force with respect to distance during collission =

= 2*0.5*mass*([travel speed]^2) / (collission length)

mean force with respect to distance =

= 2*0.5*mass*([travel speed]^2) / ([collission length]+[travel length])

limit of mean force with respect to distance as [(collision length) / (travel length)] approaches 0 is =

= 2*0.5*mass*([travel speed]^2) / ([travel length])

= mass*([travel speed]^2) / ([travel length])

Start Side Note

the mean force with respect to distance is half the mean force with respect to time when you assume collission length and collision time are both insignificantly small compared to travel length and travel time.

See Article

http://teachingthenarrowway.blogspot.com/2021/12/average-with-respect-to-time-vs-with.html

http://web.archive.org/web/*/http://teachingthenarrowway.blogspot.com/2021/12/average-with-respect-to-time-vs-with.html

End Side Note

Now Let's instead assume there is a three dimensional object of a cube of length L and instead multiple particles collide into the walls in any one of six directions or three orthogonal / perpendicular directions and there opposites each of those six directions being perpendicular to one of the six faces of the cubes.  In this case we will assume the particles do not move any other direction than those six directions to make the math easier so that in each case it will work mathematically similar to the one dimensional case above.  That is we will assume the particles will only collide with the faces of the cube moving in a direction perpendicular to the face they hit making the collission calculatable as a one dimensional problem in each case.  Let us also assume the particles do not collide into each other or do not effect each other if they were to collide into another particle but "phase through" each other or act as though having "no clipping" with respect to each other but only collide with cube faces/walls or only experience collission forces through cube faces/walls and not other particles.  Additionally we shall assume all particles have the same speed except during collissions even though in reality their would be a distribution of different speeds at most temperatures people normally experience.

Temperature = Average Kinetic Energy per molecue

(Travel Speed)^2 = Kinetic Energy per molecue / mass per molecue =

= Temperature / (mass per molecue)

Limit as [(collision time) / (travel time)] approaches 0 of (Average Force per Molecue) with respect to time  = 

= 2* (mass per molecue) *([travel speed]^2) / (L)

= 2*(mass per molecue)*[Temperature / (mass per molecue)] / L

= 2*Temperature/L

From now on I shall assume collission time is negligible and refer to force as the force calculated using the calculus limit above and as measured as on average with respect to time

Total force from all molecues = 

= Force per molecue * Density * Volume / (mass per molecue)

 = Force per mole * Density * Volume / (mass per mole)

= (2*Temperature/L) * Density * Volume / (mass per mole)

Surface Area of a cube = 6*(L^2)

Volume of a cube = L^3

Pressure = Total Force / Surface Area =

(2*Temperature/L)*Density*(L^3)/[(mass per mole)*(6*[L^2])]

Pressure = Temperature*Density/[3*(mass per mole)]

N = Density*Volume/(mass per mole)

PV=NrT

P*V = r*Temperature*Density*V/(mass per mole)

P = r * Temperature*Density/(mass per mole)

Temperature*Density/[3*(mass per mole)] = r * Temperature*Density/(mass per mole)

r = 1 / 3

I remember getting  a different answer of r = 2 / 3 when I calculated this in high school.  I decide to search for the phrase unitless gas constant online and see if anyone actually calculated a unitless value or if I am the only person to ever do so.  Apparently someone else also got 2/3 which is different than the 1/3 (or 1/6 because I calculated force two different ways based on average force as a function of length vs average force as a function of time) value I calculated this time but the same as I remember calculating in high school.

https://duckduckgo.com/?q=unitless+gas+constant&ia=about

https://en.m.wikipedia.org/wiki/Talk:Gas_constant#2%2F3_cut_-_ref_please

http://web.archive.org/web/20211215070129/https://en.m.wikipedia.org/wiki/Talk:Gas_constant#2%2F3_cut_-_ref_please

One might conclude that there should be different pressure depending on the shape of the container if it has a different volume to surface area ratio than that of a cube since the calculations were made using a cube shaped container but an assumption was made molecues do not experience force when they collide with each other only the container holding them in the calculations above.  If you remove the assumption of lack of molecular collission force except against the container walls the molecues would travel a much shorter distance between collissions.  You can imagine if there are N molecues in the container then imagine the container is made of N cubes,  the molecues would each inhabit a average volume of a cube shaped like the volume of the container / N and travel on average a length of the cube root of the (volume of the container divided by N) and have a average surface area of the cube shaped zone they move around in equal to 6 times the square of the cube root of the (volume of the container divided by N) you would end up with the same results as calculated above for the average pressure and force from these molecular collissions by partititioning a non cubed shape into many cubes.  

It might make more sense to assume the molecues typically inhabit a sphere shaped shape than a cube but a sphere which has a diameter equal to the length of a side of a cube has an equal surface area to volume ratio to that of a cube but would have a smaller surface area and volume than that cube requiring more spheres to fit in the same container if they each had a diameter equal to a side length of a cube as such it would result in a slightly different unitless constant number for R, especially if the molecues were considered to be able to move in more than six directions and a distribution of speeds rather than all moving at the same speed except when colliding.  

Pressure * Volume = Force/Area * Length/Area = Force * Length = Energy

Number of Moles * Temperature = Number of moles * Kinetic Energy per mole = Energy

Some number of Joules  = PV = rNT = r* some number of Joules

Some number of calories  = PV = rNT = r* some number of calories

r = some number without units

Even though r is technically unitless it is listed as a ratio of several units which cancel out each other to allow people to convert units from one type to another.

Surface Area / Volume for a cube of side length L

(6 L^2) / (L^3) = 6 / L

Surface Area / Volume for a Sphere 

(4*pi*r^2)/(4*pi*(r^3)/3) = 3 / r

(pi*D^2)/(0.5*pi*(D^3)/3) = 6 / D

Surface Area for a E*L by F*L by G*L rectangular solid

2*(EF+FG+EG)*(L^2)

Volume for a E*L by F*L by G*L rectangular prism

 E*F*G*(L^3)

Surface Area / Volume for a E*L by F*L by G*L rectangular prism

2*(EF+FG+EG)/(E*F*G*L)

Make a rectangular solid that is not a cube with the same surface area / volume as a cube

Let 2*(EF+FG+EG)/(E*F*G) = 6

When E = 2 and F = 1

2*(2+G+2G) / 2G = 6

12 G = 4 + 6G

6 G = 4

G = 2 / 3

2*(2+[2/3]+[4/3]) / [4/3] = 2*4 / [4/3] = 6

Let L = 1 inch

1 inches by 2 inches by 2/3 inch

volume = (4/3) inches^3

surface area = 2*([2*1]+[2*2/3]+[1*2/3]) inches^2 = 8 inches^2

8 inches^2 / (4/3) inches ^3 = 6 inches ^ -1

1 inch by 1 inch by 1 inch cube

6 inches ^ 2 / 1 inch ^ 3 = 6 inches ^ -1

Copyright Carl Janssen 2021

In some video games, noclip mode is a video game cheat command that prevents the first-person player character camera from being obstructed by other objects and permits the camera to move in any direction, allowing it to pass through such things as walls, props, and other players.

Noclipping can be used to cheat, avoid bugs (and help developers debug), find easter eggs, and view areas beyond a map's physical boundary.

http://web.archive.org/web/20170520115201/https://en.m.wikipedia.org/wiki/Noclip_mode

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/v/antiderivative-of-x-1

http://web.archive.org/web/20190515181746/https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/v/antiderivative-of-x-1

https://socratic.org/questions/what-is-the-antiderivative-of-ln-x-4

http://web.archive.org/web/20211216034307/https://socratic.org/questions/what-is-the-antiderivative-of-ln-x-4

In the kinetic theory of gases, the mean free path of a particle, such as a molecule, is the average distance the particle travels between collisions with other moving particles. 

https://en.m.wikipedia.org/wiki/Mean_free_path

http://web.archive.org/web/20220629235820/https://en.m.wikipedia.org/wiki/Mean_free_path

https://en.m.wikipedia.org/wiki/Kinetic_theory_of_gases

http://web.archive.org/web/20220513084951/https://en.m.wikipedia.org/wiki/Kinetic_theory_of_gases

Why you should be able to skip high school geometry and go straight for trigonometry

 It was common in the late 20th century and early 21st century (AD/ACE) for high schools and colleges to teach pre algebra followed by alegebra then geometry, then trigonemtry (or Algebra 3 / Triginometry) then precalculus and finally a course equivelent to AB and BC AP calculus after that there are several calculus courses that all require a course equivelent to AB and BC calculus as prerequisites.

Pre algebra was an unnecesary course because it was a mixture of the math taught before Algebra in other math classes and Algebra that you would take a second time when you take the Algebra course.  Thus if you completed all the math classes that were prerequisites for Pre Algebra you could skip it and go straight to algebra and there would be nothing you would be taught in Pre Algebra that was not either taught in Algebra or the prerequisite courses for prealgebra that you would miss.

Precalculus was a combination of Algebra 3 trigonometry and AB calculus with the exception of the possible inclusion of matrixes and probability in Alegebra 3 and or Precalculus being included in one but not the other.   If matrixes and probability are included in both Algebra 3 Trigonometry and Precalculus then there is nothing someone would miss by skipping Precalculus and going straight to AB calculus from Algebra 3 Trigonometry.  If Matrixes and Probability were not included in both Algebra 3 Trigonometry and Precalculus then there is nothing someone would miss by skipping Precalculus and going straight to AB calculus from Algebra 3 Trigonometry.

The reason for being able to remove Pre Algebra and Pre Calculus courses and let someone skip them is overlapping and redundant teaching material with zero new teaching material added.  But there is a diffetent reason all together for the lack of necessity of the high school or college geometry course in that sequence in addition to any overlapping material.

The real life practical purpose of geometry is to measure distances or lengths of paths, distances between objects or lengths of objects, locations (coordinates) of objects, volumes of objects and cross sectional and surface areas of objects.  All that can be done using material usually taught in high school algebra, trigonometry and calculus classes without ever needing to take a high school geometry course.  If you understand caartesian coordinates taught in algebra class, polar coordinates taught in trigonometry and or calculus class and the meaning of the sin, cos, tan and cotangent functions and there inverses as well as what radians are and the pythagorean theoreom taught in trigonometry class you will be able to do every one of the practical purposes I have listed that you would be able to do taking a geometry class.  The only one of those things you might learn in calculus that you might not learn in trigonometry is polar coordinates which really should be taught in trigonometry before AB calculus because it is more of a trigonometry related thing.  Now there are some of those practical things I listed you might learn to do in calculus that you would not learn in high school trigonometry but you would not learn them in high school geometry either.  Examples would be learning how to calculate the surface area or cross sectional area or volume of certain shapes by integration or the distances of certain paths that are not a single straight line segment by integration.  Now there are some useful things involving geometry people might learn like names of shapes but people usually do not learn those in high school geometry but in other classes prior to high school geometry.  In Geometry class you might learn complicated arcane and obscure ways to measure those practical things I listed in very specific special cases that might not be taught in trigonometry but in trigonometry you will learn general wide reaching methods to do all those things you can do in geometry which will be easier to remember because you do not have to create a special case to figure out each thing but can simply figure out the coordinates of things using trig functions then use those coordinates to get the desired measurements.

* Start side note

For further reading about how to get trigonometric measurements by means of algebra with casrtesian and polar coordinates without geometry class you can read the following article in progress

Tangent of the average of two angles and other trigonometric identities derived from a combination of it and the pythagorean theoreom

http://web.archive.org/web/*/http://teachingthenarrowway.blogspot.com/2022/01/tangent-of-average-of-two-angles-and.html

http://teachingthenarrowway.blogspot.com/2022/01/tangent-of-average-of-two-angles-and.html

* End side note

But what about the philosophy of using axioms taught in high school geometry being useful to learn how to use logic to make practical decisions.  This so called philosophy taught in high school geometry is the most important reason it should be abolished except perhaps for those who wish to study how cultic thinking works.  High School Geometry is full of the bad kind of dogma that is presuppositions that one is not permitted to question, as opposed to stating presuppositions you use to come to a conclusion but acknowledging the possibility your presuppositions maybe wrong.  The starting point is there is a finite number of assumptions the student starts with called axioms and the claim is made that all geometric proofs in the geometry class can and will be taught either by using only those axioms or other proofs derived only through those axioms.  The student is given a list of those axioms at the beginning of the course and expected to derive all proofs assigned as homework only through those axioms or through other proofs they have derived eventually tracing back to a point of only through those starting axioms.  The fundamental problem with this is in reality assumptions are made to derive these proofs that are not in the list of initial axioms but the student is not permitted to admit that additional assumptions are required other than the axioms initially listed if you say another assumption is needed for the proof that is not listed in the initial list given at the beginning of the course that is classified as a thought crime and the problem is marked as wrong.  The type of erroneous methodology of proofs in high school geometry class influenced most participants (who mostly were not previously educated about cult psychology to develop a resistance to the undue influence) towards pseudomathematics, pseudoscience, pseudologic and magical thinking through the act of saying and or writing things in order to agree with the consensus of an authority figure even if those things are not true.  

In the Asch conformity experiment people were more likely to claim a untrue statement was true if someone else first claimed the same untrue statement was true.

The Asch conformity experiment was an experiment where volunteers were told a false answer about the length of a line segment then asked what length the line segment was.  It was found that when a unanimous group of people gave a false answer first people more frequently said the same measurement as the false answer they were previously told instead of the correct measurement than under other circumstances.

 Something similar to the Asch conformity experiment is replicated in geometry classes where the teachers assign what assumptions maybe used and students are not allowed to pick the assumptions they use for themselves and describe which assumptions they use and how and why they used them.  Even if the teachers claims about what assumptions are needed to prove a genuinely true statement is true are false by ommission or commission the students will (or more accurately have in the past implying others will in the future) more ftequently still give the same answer as the teacher than if they never heard the teachers claim.  False by ommission in this context would be where the teacher claims that such is the exact minimum list of assumptions required to validly prove a true claim when actually given the context on the list the teacher gives additional assumptions need to be added.  False by commission in this context would be to claim a assumption is needed to validly prove a true statement when it is not needed in the context of the other listed assumptions, that is if all the other assumptions on the list were included but that assumption was removed it would still be a valid proof of a true statement.  In addition a teacher may sometimes claim a false statement is true or a true statement is false and the students will more ftequently give the same answer as the teacher.  If the students did not first hear the teacher make a false claim or say a true claim is true based on logic that was not valid the students would be much less likely to make the same error when investigating if a statement is true independently in an ungraded environment without seeing someone else's example first.  Remember in geometry class people are not graded for right or wrong answers but they are graded for right or wrong reasoning.  

According to the way this type of geometry class is done the reasoning should be in agreement with the reasoning predefined in the curriculum before the student even started the class in order to not be marked as wrong or less than an A or 100% grade for a set of problems.  One of the fundamental problems is the assumption of minimum axioms that is the foundation for all reasoning in high school geometry classes of the type defined in this essay/article/manifesto is usually or maybe even always wrong based on a claim of being complete when more assumptions are actually needed in reality.  Say you claim the teacher or textbook is missing an assumption when they show how to do a geometric proof which was an assigned homework or test problem and that assumption is not in the axiom list or derived from the initial axiom list alone and you will get your problem marked as wrong.

If a list of five assumptions were given to reach a conclusion and you were asked if these five assumptions alone with nothing added or removed were valid to show the conclusion was true or untrue and nobody told you the answer beforehand and you were not given a hint what answer someone else came to and nobody else would see or grade your answer this would not be so similar to Asch conformity.  But in the case of geometry class the teacher starts by listing a certain number of assumptions and says they are sufficient.  According to the principle learned in the Asch conformity experiment by giving you the answer first people are more likely to verbally say the same answer they were first given by someone else even if the answer they were given is false.   Geometry classes of this sort do not start with the question of if those axioms are sufficient to prove the proofs but the statement that all the proofs you are required to prove in the class can be proved with those assumptions and no more excluding that which is derived from those assumptions alone.  Nobody in their right mind would believe no more assumptions will be needed based on independent thinking without someone else first telling them no more assumptions would be needed.  Those who are first told no more assumptions will be needed to prove the proofs in the book believe so (or have said they believe so) without even first reading the entire book more often than they should by which I mean more often than never.  Geometry classes of this sort are like religious instiuitions such as Churches or Mosques where they far too many members say they believe every word in a certain book such as a particular Bible or Quran or book of Mormon are true without ever having read the entire book.  Many self proclaimed Muslims can not read Arabic but claim every statement in the original Quran manuscript in Arabic is 100% true and many people who say they are Christian at Churches say every statement in the original Bible manuscripts of a particular Bible Canon are true without having even read an entire translation of it.  It is very different to have read a translation of the Bible and say you have found zero historical claims in it that you can confirm with great certainty to be false when correctly translated than to have never even read it and to claim every statement in it is true even statements you have not read.  Yet some geometry teachers will give their testimony to the axioms as being sufficient for all proofs in the assigned geometry book and far too many people will believe them without reading the entite book.  I am not saying to read an entire geometry book but do not give me your testimony of the sufficiency of the axioms to prove every proof in the book if you never read the entire book.

Copyright Carl Janssen 2021, 2022

https://en.m.wikipedia.org/wiki/Asch_conformity_experiments

http://web.archive.org/web/*/https://en.m.wikipedia.org/wiki/Asch_conformity_experiments

A 2003 effort (Meikle and Fleuriot) to formalize the Grundlagen with a computer, though, found that some of Hilbert's proofs appear to rely on diagrams and geometric intuition, and as such revealed some potential ambiguities and omissions in his definitions.[11]

[11] On page 334: "By formalizing the Grundlagen in Isabelle/Isar we showed that Hilbert's work glossed over subtle points of reasoning and relied heavily, in some cases, on diagrams which allowed implicit assumptions to be made. For this reason it can be argued that Hilbert interleaved his axioms with geometric intuition in order to prove many of his theorems."

http://web.archive.org/web/20210508113205/https://en.m.wikipedia.org/wiki/Hilbert%27s_axioms

Euclid's list of axioms in the Elements was not exhaustive, but represented the principles that seemed the most important. His proofs often invoke axiomatic notions that were not originally presented in his list of axioms.[23]

[23] Heath 1956, p. 62 (vol. I)

http://web.archive.org/web/20211209025416/https://en.wikipedia.org/wiki/Foundations_of_geometry

Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally, this has meant using only the first four of Euclid's postulates, but since these are not sufficient as a basis of Euclidean geometry, other systems, such as Hilbert's axioms without the parallel axiom, are used.[1] The term was introduced by János Bolyai in 1832.[2] It is sometimes referred to as neutral geometry,[3] as it is neutral with respect to the parallel postulate.

[1] Faber 1983, pg. 131

[2] In "Appendix exhibiting the absolute science of space: independent of the truth or falsity of Euclid's Axiom XI (by no means previously decided)" (Faber 1983, pg. 161)

[3] Greenberg cites W. Prenowitz and M. Jordan (Greenberg, p. xvi) for having used the term neutral geometry to refer to that part of Euclidean geometry that does not depend on Euclid's parallel postulate. He says that the word absolute in absolute geometry misleadingly implies that all other geometries depend on it.

http://web.archive.org/web/20211209025836/https://en.m.wikipedia.org/wiki/Absolute_geometry

No one should be taxed to pay for child support

Mothers should not be required to pay child support to the father if he breaks up (or divorces) with her because he is not stuck taking care of the child and can allow the mother to take care of the child or if she is a unsafe caretaker or unwilling to be a caretaker he is still not stuck taking care of the child and can put the child up for adoption.  If he refuses to put the child for adoption and also refuses to allow the mother to take care of her own child then he should be required to pay.  Mothers should not be required to pay child support for a child they are not allowed to take care of.  Mothers should not be required to pay any child support for a child they are forbidden to see part of the time in the case of split custody

Fathers should not be required to pay child support to the mother if she breaks up (or divorces) with him because she is not stuck taking care of the child and can allow the father to take care of the child or if he is a unsafe caretaker or unwilling to be a caretaker she is still not stuck taking care of the child and can put the child up for adoption.  If she refuses to put the child for adoption and also refuses to allow the father to take care of his own child then she should be required to pay.  Fathers should not be required to pay child support for a child they are not allowed to take care of.  Fathers should not be required to pay any child support for a child they are forbidden to see part of the time in the case of split custody.

The government should not tax people to pay for taking care of children they are not allowed to take care of.  Single mothers and single fathers and adoptive parents should not get paid for choosing to be a parent through the taxation of people who are not allowed to take care of that child.

The person or people who take care of a child influence the child's thinking and worldview and behavior and only people who are responsible enough to plan how to economically (providing food, housing, etc. not necessarily money) support a child without taxing other people should be granted the privelege of taking care of a child.

Even if this sometimes means both biological parents lose access to funds and neither can take care of their own child economically after a break up or divorce and a third party adopts their children instead this is still an improvement over coerced child support payments, because it means more responsible people will raise the child in most cases, resulting in a child that makes better life decisions in most cases.

People should not pay taxes to send other people's children to public schools or daycare centers.  Responsible parents would have the time to home school if they are not required to work extra hours to pay for taxes to send other people's children to public schools.  Both parents working is not a valid excuse for public schools because at least one of two parents could choose not to be employed while the other one is working and still have enough resources to support the family if the parents were not collectively coerced to work extra hours through taxation to send other people's children to public school.

Although both biological parents might plan a means to be economically sufficient to support a child as a team, unforeseen circumstances such as being fired from a job for refusal to obey unethical orders of an employer may occur.  It is better therefore not to put ones primary means of economic sufficiency on an employer so that an employer can not threaten to take away your means to support your children if you do not follow unethical orders.  It is better to grow your own food and have your own means to produce clean fresh water.  In agricultural societies having more children usually meant more people that could help grow food.  None the less sometimes unforeseen factors occur even in agricultural societies where in spite of responsible economic planning of a couple before deciding to become biological parents disasters such as bad wrather, earthquakes or fire (not caused by negligence) may occur causing local famines or local crop damage and insufficient food and or drinkable water.  In such cases people may voluntarily provide charity or donations if they believe the people were responsible parents this is completely different than forcing other people to pay for child support.  Occassionally asking for donations to take care of your family in a time of unexpected need is very different than to plan to live off coerced child support payments as a regular and ongoing thing for the entire duration of the time you take care of your biological children.  In other cases a malicious third party may deliberately do actions that cause economic harm to biological parents such as burning their crops, in such cases it maybe reasonable to require them to pay for economic damage but this is not the same as requiring to pay for child support because they are not paying for the fact that other people had children but paying for the fact that they maliciously destroyed someone else's food supply.

If an adoptive or biological family is abusive a child should have a right not to be adopted by them anymore there are other people that can adopt them.  Nobody should be coerced to adopt other people's children but plenty of people are willing to adopt other people's children.

I am not here saying people should refuse to receive government subsidies to get extra resources to take care of children.  I am saying giving people subsidies to take care of children should not be used as an excuse to validate the moral legitamacy of coerced taxation or coerced childcare payments.  In cases where refusing to receive funds given by government agencies does not return the money to the taxpayers who were taxed with the excuse of raising money to pay for those funds the act of choosing to receive such funds on a individual (not policy) basis does not coerce people to pay for child support.  However if someone directly forces a ex spouse (who they initiated divorce against) to pay child support where as they could choose not to bill the ex spouse for child support this is a completely different matter.  If the ex spouse was divorced for malicious non defensive domestic violence and the violence was real the ex spouse should be in jail not out of jail employed and paying child support.

Copyright Carl Janssen 2021

https://grammarhow.com/peoples-or-peoples/

http://web.archive.org/web/20210118194052/https://grammarhow.com/peoples-or-peoples/

The cult of college

 https://duckduckgo.com/?q=universities+are+corporations&ia=web

https://duckduckgo.com/?q=colleges+are+examples+of+total+institutions&ia=web

https://duckduckgo.com/?q=colleges+are+indoctrination+centers&ia=web

https://en.m.wikipedia.org/wiki/Total_institution

http://web.archive.org/web/*/https://en.m.wikipedia.org/wiki/Total_institution

https://townhall.com/columnists/justinhaskins/2019/01/28/americas-public-schools-have-become-socialist-indoctrination-factories-n2540323

http://web.archive.org/web/20190128090804/https://townhall.com/columnists/justinhaskins/2019/01/28/americas-public-schools-have-become-socialist-indoctrination-factories-n2540323

https://illinoisfamily.org/education/illinois-indoctrination-centers-government-schools/

http://web.archive.org/web/20210127223544/https://illinoisfamily.org/education/illinois-indoctrination-centers-government-schools/

https://theamericancitadel.com/2017/12/13/public-schools-communist-training-centers/

http://web.archive.org/web/*/https://theamericancitadel.com/2017/12/13/public-schools-communist-training-centers/

https://quillette.com/2017/01/02/the-university-as-a-total-institution/

http://web.archive.org/web/20170103051532/https://quillette.com/2017/01/02/the-university-as-a-total-institution/

https://findanyanswer.com/is-college-a-total-institution

http://web.archive.org/web/20211113052345/https://findanyanswer.com/is-college-a-total-institution

Turd Flinging Monkey's Political Trichotomy

 Turd Flinging Monkey's Political Trichotomy

1 Freedom

2 Equality

3 Stability

Not everyone shares the same values in life when it comes to politics and money there are three common values that are mutually exclusive.  You can not have 100% of all three at the same time or even 100% of two out of three at the same time but you can mix and match.  

Complete economic freedom can not co exist with complete equity because the freedom to make different choices will result in unequal wealth

By Economic Equality I do not mean Equality of opportunity in the context of this article.  Equality of opportunity is closer to Economic freedom than Economic Equality but not neccessarily the same as Economic freedom.  Economic freedom may not result in equality of opportunity because having more money gives people more opportunities to do business.  Equality of opportunity is not the same as economic equality because not all people choose to live up to their maximum economic potential with the opportunity they have.  If two identical twins both have the same economic opportunity and one person works "smarter" and also puts in more time and effort to making money they will not have equal amounts of money in a monetary society with equality of opportunity.

Some people make a distinction between Economic Equality and Equity.  If you gave every one the exact set of the same food items with the exact same quantities that add up to the exact same number of calories that would be economic equality in terms of giving food but would not be equity.  Equity is based on giving according to "needs" where as equality in this context is giving identical amounts irregardless of needs.  In the case of equity you might give people with a higher metabolism more food and those with a lower metabolism less food.  Perhaps you could have both equality and equity if you gave everyone an equal amount of food that is based on the caloric expenses of the individual with the highest metabolism in the group such that both everyones "needs" were met and also everyone was given an equal amount.  If you gave every individual in a group the same amount of food equal in calories to the average mean caloric expense per person in that group you would have equality but not equity because the "needs" of the individuals with above average caloric expense would not be met and they might start starving if they are not obese and not spending calories with "unnecessary" work (not needed for survival) that they could choose to reduce.  If the individuals have different metabolisms and everyone is given an equal amount of non perishable food items  that are sufficient to meet the needs of even the individual in the group with the highest metabolism and both economic equality and economic equity is achieved in terms of how much food each individual in a group is given then those with a lower metabolism would be able to save more non perishable food items than those with a higher metabolism and so even though economic equality would be achieved in how much food people are given there would still be economic inequality in the amount of extra food saved for an emergency each individual has.  If everyone was given equal income, people would still have unequal savings if they have unequal spending.  It is very much difficult then to have economic equality because equality in all things can not exist to force equality to exist in one measureable criteria might remove it in another.  To make things simpler when people say they value economic equality in many cases they may simply mean they value government "welfare" programs and very rarely means they value two measurable economic quantities being equal.

Anarcho Capitalism is economic freedom without economic equity/equality

Statist Communism is economic equity/equality without economic freedom

Negative income tax is Partial Economic Freedom plus Partial economic Equality

Negative income tax is Universal Basic Income plus Flat income tax without any other government programs to help the poor (other than Universal Basic Income) and without corporate welfare and without tax deductions

Social Security is Partial Economic Equality/Equity plus Partial Economic Stability

The elderly who have already made a fortune and do not want to lose it often prefer the economic stability of maintaining that fortune even if it means a lack of economic freedom for the youth and a lack of economic equality/equity for the youth to receive the same benefits as the elderly.  The elderly who have spent their fortune and are no longer in good mental or physical health to earn more often prefer economic equality/equity compared to the healthier youth who have more earning potential through labour (by which I mean the elderly receiving equal or equitable pay compared to the youth without the elderly doing equal or any [future] labour compared to the youth)

Since the three values are mutually exclusive in their fullest forms people who value economic freedom find those who value economic equality/equity at the expense of economic freedom to be problematic when such indivuduals support violent means to equalize wealth.

A simple solution would be for those who support economic freedom to separate from those who support economic equality/equity so they do not quarrel due to conflicting values. 

Those who support economic freedom would have no problem allowing those who support economic equality/equity to have their own commune where everything is distributed equally/equitably so long as they are not forced to join the commune.  Those who support economic freedom have no problem with those who support economic equality/equity living out their values so long as those who support economic freedom are not required to live out the values of economic equality/equity.

 But often those who support economic equality/equity do not want to permit those who support economic freedom to leave and live in a separate community from them because then they could not take their stuff.  Those who support economic equality/equity often have a problem with allowing those who support economic freedom to live out their values because then they could not take their stuff.

Copyright Carl Janssen 2021

duckduckgo.com/?q=political+trichotomy&ia=web

observablereality.com/political-trichotomy/

http://web.archive.org/web/20211112075222/https://www.observablereality.com/political-trichotomy/

Political Trichotomy: Cant We All Just Get Along?

by Turd Flinging Monkey

https://archive.org/details/BitChute-RG-bAcyWbsg

Political Trichotomy Cant We All Just Get Along

youtube.com/watch?v=vQmWfKXWhSM

http://web.archive.org/web/20211112080604/https://www.youtube.com/watch?v=vQmWfKXWhSM

Turd Flinging Monkey Political Trichotomy All Systems Fail (mirror)

francis chow

youtube.com/watch?v=318KHpJ8bHU

http://web.archive.org/web/20211112081452/https://www.youtube.com/watch?app=desktop&v=318KHpJ8bHU

Turd Flinging Monkey Political Trichotomy The Moderate Right (mirror)

francis chow

https://m.youtube.com/watch?v=oYCgbjYqEiA

http://web.archive.org/web/20211112081708/https://www.youtube.com/watch?app=desktop&v=oYCgbjYqEiA

Turd Flinging Monkey Political Trichotomy The American State Religion (mirror)

francis chow

https://m.youtube.com/watch?v=9qPZ_cktO20

http://web.archive.org/web/20211112082134/https://www.youtube.com/watch?app=desktop&v=9qPZ_cktO20

Moral value not to murder may derive from the desire not to be murdered

Moral value not to murder may derive from the desire not to be murdered nor killed

Morality is both subjective and objective

Morality is both relative and absolute.  Some people say morality is either relative or absolute and can not be both but they are simply wrong

Even though morality is relative to the individual it is still very much objective and absolute.  Relativity does not contradict absoluteness or objectivety.  The elevation of the top of a building above sea level is an absolute and objectively measurable distance but it is still relative to sea level because you could also measure it's elevation relative to another location such as the height above the buildings parking lot for instance

If you do not want to be murdered you would desire to live in a society where other people have a moral value of not wanting people to be murdered to the point where they are willing to either imprison, exile/banish or execute murderers or attempted murderers.

But living in such a society would result in arrest, banishment or execution for you if you commit murder or attempt to commit murder

Even if you do not have a moral prohibition of murdering other people innately in your moral code, you would choose to have a moral prohibition against murdering other people in your moral code if you do not want to be killed, murdered or imprisoned out of a desire to be in a society where murderers are prosecuted combined with a desire not to be imprisoned, executed or banished out of such a society (as banishment would be certain death when the only remaining alternative societies to leave to have no prohibition on murder)

So even though not everyone might have the same moral code not to murder people most people will adopt such a moral code not to murder people if they do not want to be murdered or killed themselves and they think things through sufficiently

There are some people who do not care if they are murdered or killed and do not have any moral prohibition against murdering people in their mind.  Such people are rare but most certainly exist.  Such examples would certainly include mass murderers or serial murderers that requested the death penalty for themselves.

If everybody practiced the same universal moral code there would be no suicides so clearly morality is relative to the individual and not all people universally share practice of the same moral code 

Although practice of the moral code not to murder is not present in 100% of the society it can be widespread in a community as people who do not want to be murdered would choose to hang around people who morally object to  murdering other people.  Someone not sharing a personal moral code not to murder people would not get off the hook in such a society because they live by a different moral standard instead such a person would be imprisoned or executed or at least banished and exiled (with threat of death or imprisonment upon returning) upon committing or attempting to commit a murder in such a society precisely because other people in the society do not want to be murdered by them.

Copyright Carl Janssen 2021

In a society with property tax employment is slavery with extra steps

In a society with property tax employment is slavery with extra steps, in a society without property tax employment might not be slavery.  The combination of property tax, zoning laws and vagrancy laws create a situation in which one must be employed to pay property tax or rent to someone else who pays property tax or be sent to jail when they sleep.  One can not simply farm food and eat it without selling it while being unemployed because of property tax

Copyright Carl Janssen 2021 November 9

Probability does not exist for playing cards

 Imagine you have a deck of 52 uniquely labeled playing cards each one being different such that there are no cards which repeat the same label as another card.  Shuffle the cards "randomly" placing them in a pile facing down so that you can not see the labels and that they are in one pile of 52 items that would be drawn in a specific order and in only one order if whatever card is on top is drawn each time.  

Normally each of the unique card labels will be given a probability of 1/52 chance or (100/52) percent chance of being drawn on the first draw and all of the card labels will be assigned the exact same probability individually.

In reality there is only one card on the top of the deck of 52 cards and it has a 100% chance of being drawn when the top card is drawn, all other cards have a 0% chance of being drawn.

Forms of statistics that use probability are not scientific and not mathematical.  Forms of statistics that use probability include mathematical functions but are not truly a form of math or at least not a truthful and factually correct form of math or science in terms of accurately representing reality.

It is possible to use math without being scientifically minded in attitude or mathematically truthful.  For example someone could make a formula that the number of inches tall any and every man in Sweden is, is equal to 50 plus the number of fingers they have they could even measure many men in Sweden and find many (but not all) of them to be 60 inches tall rounded to the nearest inch and simultaneously having 10 fingers.  That would be a mathematic formula to represent height but it would not be valid math or science to do so even if the conclusion was correct for a large number of Swedish men the reasoning to arrive at such a formula would not be valid.  You could call it math if you want to but it would not be truthful math.  You could call anything in which quantities are calculated using mathematical formulas math if you want to but you really should not call probability math in the sense of being valid, reasonable, correct or truthful math.  

Statistics with probability is not valid math even though it uses mathematical functions to do calculations instead the use of statistics with probability is a religious worldview that is used by many people that label themselves as scientists.  It consists of a protocol for calculating probabilities, but as I already demonstrated with the cards example that protocol gives you the incorrect answer.

I do not have any problem with statistics without probability as you could count how many of something there is and call that statistics and that is fine.  But the use of statistics with probability such as paired and unpaired t-tests,  ANOVA tests etc. are not in line with a proper use of the scientific method even if quantities are measured and then calculations are done with those measured quantities.

Statistics with probability is not pure math it is applied math and the application of that math does not apply correctly to represent reality.

The scientific method is testable, falsifiable, observable, repeatable, accurately predictive and measurable.  The use of probability in "science" is not repeatably accurately predictive or falsifiable.

For example Newtons laws of motion will give you a single answer for kinematic problems involving the predicted location of an object at a specific time based on mathematical formula.  Those predictions do not give a distribution of probabilities of different locations but a single location for a single object at a single point in time that can be measured.  Either the object is at that location or it is not within a certain margin of reasonable error and rounding.  Newtonian laws (excluding G but including the use of g) have been shown to accurately predict the location of objects in the world we live on repeatably.  A prediction is made based on input and a output occurs the output can then be decided as either refuting the prediction or confirming the prediction within a certain acceptable margin of error that is why testing Newton's laws can be done using the scientific method because it is not a probabilistic model but is instead a falsifiable model.

When metric and a decimal number system is used with metric measurement tools the margin of what is reasonable error is not based on probabilities of distribution of measurements but significant digits.  With significant digits the range of possible measurements is explained based on the limitations of the measurement tools.  There is an upper maximum measurement and lower minimum measurement based on rounding up and rounding down to the nearest second to last digit.  An exact and precise set or range of output answers can be calculated using the values for each input rounded down or rounded up to the second to last digit with no need for probability whatsoever to determine what range is acceptable for the output.  For example if something is measured as a length of 3.15 meters it's actual length could be anywhere between a minimum of 3.1 meters and a maximum of 3.2 meters a range of acceptable outputs can be determined based on plugging in a range of input values between 3.1 meters and 3.2 meters into whatever function is used to predict the output.  There is no need in such a case to give probabilities assigned to each output value, if it is outside the range the function failed to predict and if it is within the range the function succeeded in prediction.

The scientific method is falsifiable meaning that a formula can be shown to falsely reflect reality if the output is not in the range calculated for the input.  Probabilistic statistical methods such as t tests work entirely differently and are fundamentally non falsifiable despite a false pretense of falsifiability. First an assumption of a normal distribution curve is typically assumed with no proof of such a distribution in reality although sometimes methods are used to try to test if it actually is a normal distribution curve within a certain probability.  Then based on the faulty assumption that both samples or populations are normally distributed a standard deviation and mean is separately calculated for each of the two separate groups.  Then a alpha value is arbitrarily chosen and an arbitrary decision is made as if a one tail or two tail test will be used with some fake justification as to why one or two tails is to be chosen.  It is then decided if the average mean of these two groups is different because they both have the same distribution and the difference was caused by random variance or have two different distributions caused by a non random factor.  If the two different groups have no difference in there average mean (a difference of zero) such a t test will not be needed because no matter what non zero alpha value is assigned the conclusion will be the same.  If the two groups have different means whether or not the difference between the two groups was statistically significant is based on the alpha value and number of tails if a different alpha value was chosen a different conclusion would be reached.  This testing method is claimed to be scientific and falsifible but it really is unfalsifiable because having chosen a different alpha value would change the conclusion, choosing an alpha value in advance does not magically meet the requirement of falsifiability because the alpha value is chosen arbitrarily and not by the physical limitations of the tools or any physically observable means but with how much "risk" the performer (or the performers supervisor/boss) is comfortable with.  You can not actually know if the measurements for the groups are different by random or non random causes you only allegedly get a probability that they are different making this testing method non falsifiable.

Resorting to using t tests instead of predictive formula that can be potentially falsified shows a lack of knowledge as to the subject matter of the experiment or requirement to act as though lacking knowledge in the case of just doing it for homework or for an employer or supervisor.  For example if a specific dose of medicine such as 10 mg is being tested to effect heart rate a t test could be used to determine if the control group not using the medicine has a statistically significant different heart rate than the test group using the method but this involves no chemical/physics model for how the medicine chemically influences the heart.  There is only a comparison between 10 mg and 0 mg but no function of heart rate based on the input of dosage and other variables, no prediction is made in advance as to what the heart rate will be as a function of dose such that there will be a specific heart rate for 5 mg and a different one for 10 mg or 7 mg each predicted output being a specific number for each input.  There is no predicted output at all for this kind of testing only a conclusion of a probability that the results of the two groups are different.  The output predicted for each input can not be falsified when there is no numerical prediction as to what the output actually will be.  Claiming the heart rate will be 60 bpm + 1 bpm*dosage/1mg is a testable formula but claiming the heart rate will be different with no quantity predicted as to the number of bpm is not a formula at all and therefore certainly not a testable and falsifiable formula.  Making such a claim involves no need for the presentation of mathematical formula involving chemical reactions of the drugs and this displays a fundamental lack of knowledge in the subject matter tested in such an example.

Probability based Statistics should only maybe be used when one admits they do not have a understanding of how the subject matter tested physically or chemically works.  In the long run one should not try to get a better understanding by doing more statistical tests for several years but instead start proposing formulas based on past observations then test those formula to see if they correctly predict future quantities and reject them if they do not then try testing new mathematical formula instead until a formula is found that has a trend of making successful predictions.  Probability based statistics can be done rarely and occassionally in the short run just to get a guess as if doing something has any effect at all but should be replaced with the use of formula instead in the long run.  Probability based statistics should not be the primary basis for medicine. 

Look at the percentage of scientific journal articles in industrial engineering, quality control engineering, biology, psychology, sociology and health related fields that use statistical tests instead of formula with predicted output as a function of input being tested and you will understand that the early 21st century and the 20th century were metaphorically in the dark ages when it came to science and people were publishing religion disguised as science in many of the articles in scientific journals during this time period.

Look at the curticulum of graduate programs almost always requiring statistics classes for graduate students to take during graduate school but rarely requiring pure math courses to take during graduate school and the proportion of thesis projects in industrial engineering, psychology, sociology and health science related degrees using statistics instead of mathematical formula and understand that in that time period proper scientific research methodology was not being taught in many science, health and industrial engineering classes.

Copyright Carl Janssen 2021 October 22