[Yahya A.Sharif (OP)]

Zeno's paradoxes-especially the *Dichotomy* (infinite steps to start moving) and the *Arrow* (motionless at every instant)-have haunted philosophy and physics for millennia. Calculus "solved" them mathematically with limits and infinitesimals, but what if the core issue is deeper? What if continuity itself is the illusion? 

A radical new framework proposes exactly that. By embracing inherent relativity and discrete "virtual units," these paradoxes vanish without infinities or contradiction. Measurement is Relative 
Distance and time have no absolute units. "1 meter" is just "100 cm" or "1000 mm"-the *number* depends entirely on your chosen unit. Zeno's infinite subdivisions arise only when we rigidly fix a unit (e.g., meters) and insist on slicing space/time endlessly within that frame. But what if we redefine the units themselves? 

Introducing "Virtual Units" 
Imagine an object moving 1 meter. Zeno says it must cover: 
`1/2m → 1/4m → 1/8m → ...` (infinite steps). 

The breakthrough: Redefine each segment as its own unit: 
- Let `1y = 1/2 m` → Move 1y
- Let `1z = 1/4 m` → Move 1z 
- Let `1u = 1/8 m` → Move 1u
Motion becomes a finite/countable sequence of discrete transitions.No infinite tasks-just unitary steps. The "infinite regress" dissolves because units adapt relatively to the scale. 


The Arrow Paradox (Frozen in time?):
   - Classical view: Velocity = `0/0` at an instant → "motionless." 
  Instantaneous velocity is mathematically undefined, not zero. Motion is a potential state defined by mass/kinetic energy. At each instant, the arrow has the potential to move-realized over any non-zero time interval. We can't determine whether the object is moving or not without observing it over a non-zero time interval.

Broader Implications 
 Echoes quantum discreteness (Planck scale) and relativity (observer-dependent units). 

Conclusion:
Zeno wasn't wrong-he revealed the flaw in assuming absolute continuity. By treating units as relative and motion as discrete transitions, virtual units restore logical coherence to motion while aligning with modern physics.

Discrete Space-Time and Virtual Units: A Modern Resolution of Zeno's Dichotomy and Arrow Paradoxes

[alancalverd]

Zeno was wrong. Each subsequent discrete step takes a decreasing amount of time, so if the zillionth step takes 1/zillion seconds you only have to wait another 2 zillionths of a second to go twice as far and pass your destination. Ergo you must at some time have reached your destination.

[Yahya A.Sharif (OP)]

Zeno was wrong. Each subsequent discrete step takes a decreasing amount of time, so if the zillionth step takes 1/zillion seconds you only have to wait another 2 zillionths of a second to go twice as far and pass your destination. Ergo you must at some time have reached your destination.

The problem is still  that 2-zillionths of a second will itself be halved, then quartered, then eighth-ed, and so on..And it will move a fraction of the distance during each fraction of those 2-zillionths of a second.