Part 1: FULL INTRO
The goal remains the application of 'derivatives of displacement' to describe the spread of COVID-19. The points made will apply to any application over time (not just virus spread).
This charts focus is on COVID19's "snap". Snap is the 4th derivative of displacement:
Rate of spread (how many each day)
Velocity of spread: Change in Rate over time
Acceleration of spread: Change in Rate over time
Jerk of spread: Change in Rate over time
Snap: Change in Jerk over time
Snap is explosive change best described as "Oh Sh-t!"
Examples of snap include :
Waterfall.
Take off.
Flooring it.
Rocket launch.
Peak violent vomiting
Roller coaster with 360 loop.
COVID19 spread as of Nov, 2020. (Black histogram in upper right chart)
Why should I care?
Acceleration, Jerk and Snap can be evaluated together when expressed in standard deviations. 95% of measurements fall between -2 STD and +2 STD away from their mean mean (assuming a normal distribution).
The lower right chart presents the derivatives in terms of STD's. At the time of writing they are all above the midline (i.e. all positive). In terms of "stopping the spread" of the virus consider the difficulty in stopping any of the 'snap examples' above.
A job for superman? Superman was said to be "faster than a speeding bullet". However, after leaving the barrel, a bullets velocity and acceleration are negative. Bullets slow down, while virus spread speeds up. The bullets deceleration lacks jerk or snap unless it hits a wall. Yet, on one point the bullet metaphor *is* useful:
Giving a bullet or a virus a 'head start' has an exponential impact . For a virus the head start may be time for asymptomatic spread. For a bullet its a longer barrel and more time to build velocity.(see note below).
Time Matters and the time is now
American Jerk behind COVID surge : Derivatives of displacement
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[Note on projectile velocities :
A bullet, while moving through its barrel, is being pushed forward by the gas expanding behind it. This gas was created when the trigger was pulled, causing the firing pin to strike the primer, which in turn ignited the solid propellant packed inside the bullet cartridge, making it combust while situated in the chamber. Once it leaves the barrel, the force of the expanding gas ceases to propel the bullet forth. When a bullet is fired from a handgun with a 2-inch (51 mm) barrel, the bullet only has a 2-inch (51 mm) "runway" to be spun before it leaves the barrel. Likewise, it has only a 2-inch (51 mm) space in which to accelerate before it must fly without any additional force behind it. In some instances, the powder may not have even been fully burned in guns with short barrels. So, the muzzle velocity of a 2-inch (51 mm) barrel is less than that of a 4-inch (100 mm) barrel, which is less than that of a 6-inch (150 mm) barrel.
The goal remains the application of 'derivatives of displacement' to describe the spread of COVID-19. The points made will apply to any application over time (not just virus spread).
This charts focus is on COVID19's "snap". Snap is the 4th derivative of displacement:
Rate of spread (how many each day)
Velocity of spread: Change in Rate over time
Acceleration of spread: Change in Rate over time
Jerk of spread: Change in Rate over time
Snap: Change in Jerk over time
Snap is explosive change best described as "Oh Sh-t!"
Examples of snap include :
Waterfall.
Take off.
Flooring it.
Rocket launch.
Peak violent vomiting
Roller coaster with 360 loop.
COVID19 spread as of Nov, 2020. (Black histogram in upper right chart)
Why should I care?
Acceleration, Jerk and Snap can be evaluated together when expressed in standard deviations. 95% of measurements fall between -2 STD and +2 STD away from their mean mean (assuming a normal distribution).
The lower right chart presents the derivatives in terms of STD's. At the time of writing they are all above the midline (i.e. all positive). In terms of "stopping the spread" of the virus consider the difficulty in stopping any of the 'snap examples' above.
A job for superman? Superman was said to be "faster than a speeding bullet". However, after leaving the barrel, a bullets velocity and acceleration are negative. Bullets slow down, while virus spread speeds up. The bullets deceleration lacks jerk or snap unless it hits a wall. Yet, on one point the bullet metaphor *is* useful:
Giving a bullet or a virus a 'head start' has an exponential impact . For a virus the head start may be time for asymptomatic spread. For a bullet its a longer barrel and more time to build velocity.(see note below).
Time Matters and the time is now
American Jerk behind COVID surge : Derivatives of displacement
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[Note on projectile velocities :
A bullet, while moving through its barrel, is being pushed forward by the gas expanding behind it. This gas was created when the trigger was pulled, causing the firing pin to strike the primer, which in turn ignited the solid propellant packed inside the bullet cartridge, making it combust while situated in the chamber. Once it leaves the barrel, the force of the expanding gas ceases to propel the bullet forth. When a bullet is fired from a handgun with a 2-inch (51 mm) barrel, the bullet only has a 2-inch (51 mm) "runway" to be spun before it leaves the barrel. Likewise, it has only a 2-inch (51 mm) space in which to accelerate before it must fly without any additional force behind it. In some instances, the powder may not have even been fully burned in guns with short barrels. So, the muzzle velocity of a 2-inch (51 mm) barrel is less than that of a 4-inch (100 mm) barrel, which is less than that of a 6-inch (150 mm) barrel.
