Velocities Cannot be Squared
Take any flat line. Draw parallel lines, the same length as this line, straight up from either end of this line. Connect the tops of your two new lines and you have a square. This alone is what “squaring” means.
To find the surface area of the square you have created: measure the original line in whatever length units you desire (e.gs. inches, meters) – then multiple that unit’s number by itself. The resulting product, expressed in “square inches” or “square meters,” is your square’s area.
The Pythagorean formula merely acknowledges that for every triangle possessing a right angle, squares formed out of the triangle’s two shorter sides will have a combined area equal to the area of the square formed from the triangle’s hypotenuse.
The area of circle is “Pi times radius squared.” This formula begins with a straight line drawn from the centre of a circle to its perimeter. This line becomes the base line for a square. The area of the circle will equal the area of this square multiplied by 3.14.
A velocity, or speed, is the distance travelled during a period of time, e.g. 100 kilometers per hour (kph). Velocities are expressed as fractions with the numerator representing the length travelled and the denominator representing the duration of the trip. Fractions are squared by multiplying the numerator by itself and the denominator by itself, whilst keeping the structure of the fraction in tact. Thus – one quarter squared equals one sixteenth.
Divide a cake into four pieces, then divide each piece into fourths. Velocities can be added to velocities. A cricket ball bowled at 160 kph from atop a freight train travelling 100 kph, in the same direction as the ball, will have a velocity of 260 kph.
One can multiply a velocity. One can go twice as fast by either doubling the distance travelled while keeping the time fixed; or by fixing the distance travelled and dividing the travel time in two.
Multiplying a velocity is not the same as squaring a velocity.
Distances are tangible, measurable physical lengths. Time, the universal medium of motion, can also be broken into measurable units. The units humans use to measure distance and time are arbitrary cultural conventions. This causes grave physical problems when one attempts to square them.
The following three velocities each express the same speed:
A) one mile per one minute,
B) 60 miles per one hour, and
C) 96 kilometers per 60 minutes.
The squares of these three velocity fractions, seen below, produce disparate distortions:
A) One mile per minute (96 kph)
B) 3,600 miles per hour (5,760 kph)
C) 9,216 kilometers per 3,600 minutes (153 kph)
Problems are not removed by standardizing velocities into meters per second. Consider the following:
A) One meter per second “squared” equals one meter per second
B) Forty meters per second “squared” equals 1,600 meters per second
C) Half a meter per second “squared” equals one quarter of a meter per second
(Adhering to the theo-physics foible of “squaring” the “seconds” by negative 2 produces the same results as 1 to the power of -2 is still 1.) Example A leaves the velocity unchanged. Example B yields a faster velocity than the original velocity,
while Example C yields a slower velocity. Apparently, squaring a velocity faster than one meter per second speeds up the velocity, while squaring a velocity slower than one meter per second slows down the velocity.
Is one meter per second (3.6 kph) some magical universal constant? Do these wholly arbitrary, historically-determined, cultural conventions of “second” and “meter” miraculously fall into place as a fixed melting point of motion? Nonsense!
Time cannot be squared. A “square second” is an incomprehensible, a-physical and useless construct. A “square meter” is a four-sided plane with four one-meter sides. It is not a line. It is not a distance. If it were a distance, would a “squared” meter be 2 meters long, or 4 meters long? We can multiply a meter by a natural number like two; but we cannot meaningfully multiply a meter by a meter and produce a workable distance.
You can tell the cab driver to double his speed. You cannot meaningfully tell him to square his speed. One can add, subtract, multiply or divide velocities – one cannot square them. One cannot cube them. The presence of v-squared (v2) in an equation betrays the equation as an act of mathematical obscurantism.
The ubiquitous presence of v-squared in Theoretical Physics hieroglyphics (most infamously c2) tells us all we need to know about this academic discipline.
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Kenneth Hughes
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Words fail me, so, to put it succinctly, this article is complete garbage.
I am surprised and disappointed that PSI have posted this.
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Alan
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I thought 1 April had arrived late.
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Geraint HUghes
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Interesting article but what is the point? Is he saying KE = 1/2mv(squared) cant be used to determine kinetic energy to figure out net work done on an object?
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Geraint HUghes
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So in my example above a truck moving twice as fast would have 4 times the energy.
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Herb Rose
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Velocity squared is a unit for energy just as foot pounds is a unit of torque. It cannot be separated into other units You cannot determine the weight of a bolt using the torque used to set it and its length. The fallacy of relativity is it equates energy (d^2/t^2) with mass time energy (md^2/t^2).
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Greg Spinolae
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What manner of unmitigated gibberish is this?
Is the author a policy writer for Whitehall Wasters?
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Jerry Krause
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Hi Guys,
We all make mistakes no matter how ‘brilliant’ a person has been. (https://principia-scientific.com/feynmans-blunder-part-1/) (https://principia-scientific.com/?s=Feynman%27s+blunder).
William began: “In reality (as opposed to in purely abstract mathematics) lines, and lines alone, can be squared.” Most 4th graders probably know that NUMBERS alone can be squared.
Which of you has never made a simple error like Feynman or William made and then for a while gone off on a tangent as you reasoned???
Have a good day, Jerry
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Zoe Phin
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April 1st was a while ago.
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T. C. Clark
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He added speeds…the freight train at 100 kph and a ball kicked at 160 kph…260 kph is not correct….time is variable and the speed would be close when added but not correct. C is a constant and maximum speed.
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