THE EZ CLOCK

A clock that adapts to the Sun

Solar-Relative Elastic Timekeeping System
Complete System Documentation, Version 1.2.1

Ez Clock is a solar-relative elastic timekeeping system invented by Ez Aldeen Alsubainy.

Abstract

Ez Clock is an alternative system of timekeeping in which the numerical structure of the clock remains fixed while the physical duration of its hours, minutes, and seconds changes according to the Sun. The sunset-to-sunset cycle contains 21 Ez Hours arranged into three seven-hour stages: night, morning, and afternoon/evening. Each Ez Hour contains 100 Ez Minutes, and each Ez Minute contains 100 Ez Seconds.

The three stages are numerically equal but physically unequal. Their durations are determined independently by solar geometry at the relevant geographic position, causing Ez Hours, Ez Minutes, and Ez Seconds to expand or contract with location, season, and stage of the day. Where a complete local sunrise-and-sunset cycle does not exist, the system uses the geographically nearest valid solar point determined by minimum great-circle distance.

Ez Clock is therefore not merely another display of conventional time. It defines time relative to the progression of the local solar cycle.

Origin

This section is written in the first person by the author. The numbered parts that follow are the formal specification.

I knew what the objections would be before I had finished thinking the clock through, because they are the obvious ones, and a system that cannot answer them is not a system. So I want to set out the answers here, in my own words, before the specification states them formally.

The first objection is that sunrise and sunset are not the same for everybody. Someone in a valley and someone on a hill do not see the Sun leave at the same moment. This is true, and it is not a problem, because Ez Clock does not ask what anybody sees. It calculates the angle of the Sun for a geographic position from the rotation of the Earth, its orbit, and the season. Sunset is the instant the Sun completes its passage out of that position's sky by that calculation. Sunrise is the instant it begins coming back. Picture a straight one kilometre ladder with one person at the top and their friend at the foot. They will see two different sunsets. They have the same Ez Time. They are standing in the same place as far as the Sun is concerned, and the clock follows the Sun, not the eye.

The second objection is the poles, where for months there is no sunrise or no sunset to anchor anything to. An Ez Day six months long is meaningless, and honestly it is laughable. It would destroy the hours, the minutes, the seconds and the entire daily rhythm the clock exists to express. So when a location has no complete cycle, the clock takes the nearest point that does, by shortest distance over the surface of the Earth, and it tells the user it has done so. No borders, no capitals, no chosen cities. Just the nearest place where the Sun still behaves like the Sun. It is forced rather than offered, because a solar clock without a working solar day is not a clock.

The third objection is that the seconds are not equal. They are not, and that is the invention rather than a flaw in it. I wanted three stages of the day moving in completely separate settings, each one judged by the mood of the Sun, seconds flying in one and dancing slowly in another. When you agree to meet someone at Ez 10, both of you know immediately where the Sun is standing for the other and how much of their morning is left. An hour in winter takes far more of a person's daylight than an hour in summer, and people should know that when they ask for it. The clock says so without anyone having to make the argument.

What I wanted most was to end a particular feeling. You look up, the Sun is going, and you think: the day is finished and I did nothing. That should not be possible. The approach of sunset should have been on your wrist the whole time, visible, numbered, getting closer. On Ez Clock the Sun moves on your hand.

People have read the Sun for as long as there have been people, and a stick in the ground is older than any of us. What is new here is the system laid over it: twenty-one hours instead of twenty-four, three stages of seven, sunset as zero, a hundred minutes in an hour and a hundred seconds in a minute, units that stretch and compress with the stage they sit in, and time tied to an exact position on Earth rather than to a border drawn by a government. That is my work, and the technology to calculate it and put it on a screen is what makes it a clock rather than an idea.

PART I: FOUNDATION

1. Definition

Ez Clock is a geographically local, solar-relative system of timekeeping in which the numerical structure of the clock remains fixed while the physical duration of its hours, minutes, and seconds changes according to the Sun.

Ez Clock does not attempt to make the Sun conform to a mechanical clock. It makes the clock conform to the Sun.

The system rests on four numerical anchors:

One complete Ez Day contains 21 Ez Hours, divided into three equal numerical sectors of seven:

• 0 to 7: Night
• 7 to 14: Morning
• 14 to 21: Afternoon / Evening

Their numerical lengths are equal. Their physical durations are not. That difference is deliberate and fundamental.

2. Foundational Principle

The Sun does not follow the clock. The clock follows the Sun.

Conventional timekeeping uses fixed mechanical units and allows sunrise, solar noon, and sunset to drift across the clock throughout the year. Ez Clock reverses that relationship. The solar events stay numerically fixed, and the seasons instead affect the speed of time.

3. Ez Clock Is a Clock, Not a Calendar

Ez Clock is concerned exclusively with the daily solar cycle. It is not a dating system and requires no calendar of its own. The Gregorian calendar, or any other, continues in parallel and untouched.

Ez Clock answers: Where are we within the local solar cycle?

It does not answer: What date is it?

An Ez Day begins at sunset and therefore crosses conventional midnight. This creates no conceptual problem whatsoever. The clock and the calendar are separate systems and should not be reconciled. Implementations should not attempt to define an "Ez date."

4. The 21-Hour Ez Day

There is no physical law requiring a day to be divided into 24 parts. Twenty-four is a historical convention. Ez Clock chooses 21 because it permits the solar cycle to be arranged into three structurally equal groups:

21 = 7 + 7 + 7

5. Why Three Solar Stages

Human experience of a day is not uniform. Night is not a continuation of afternoon. Morning is not an arbitrary set of mechanical hours. Afternoon and evening form a distinct phase as the Sun descends.

Ez Clock treats the daily cycle as three temporal environments:

Stage I, Night (0 to 7): sunset to sunrise Stage II, Morning (7 to 14): sunrise to solar noon Stage III, Afternoon / Evening (14 to 21): solar noon to sunset

Each stage may run at a substantially different physical speed. That is not an error. It is one of the primary functions of the system.

PART II: THE ANCHORS

6. Sunset, Ez 0

The Ez Day begins at the instant the Sun mathematically completes its descent below the reference horizon for that geographic position. At that instant the clock reads 00:00:00.

It does not matter whether civil time calls sunset 16:40, 18:05, 19:30, or 21:00. In Ez Clock, sunset is always zero.

7. Sunrise, Ez 7

The following sunrise always occurs at 07:00:00. The entire astronomical interval from sunset to sunrise is divided into exactly seven equal Ez Hours, so the physical length of a Night Ez Hour tracks the physical length of that night.

8. Solar Noon, Ez 14

Solar noon occurs at 14:00:00. This means the astronomical instant at which the Sun reaches maximum altitude for that position during the cycle. It is not conventional 12:00, it is not set by a national time zone, and it is not shifted by daylight saving.

9. Following Sunset, Ez 21 / 0

At sunset the clock reaches 21:00:00, which is simultaneously 00:00:00 of the next Ez Day.

21:00:00 ≡ 00:00:00

PART III: THE ASTRONOMICAL HORIZON

10. Sunrise and Sunset Are Calculated, Not Observed

Ez Clock does not define sunrise and sunset by what a particular person visually observes. The system is astronomical and mathematical throughout.

The clock computes the angle of the Sun relative to the geographic position. Sunset is the moment the Sun completes its crossing out of the visible hemisphere of that position. Sunrise is the moment it begins crossing back in. These are derived from:

• the geometry of the Earth,
• the geometry of the Sun,
• Earth's rotation,
• Earth's orbital position,
• the observer's latitude,
• the observer's longitude,
• and the applicable astronomical solar model.

The user's visible horizon is irrelevant.

11. Mathematical Horizon Principle

Ez Clock uses an ideal mathematical horizon associated with latitude and longitude. It does not use mountains, valleys, buildings, trees, windows, local obstructions, observer height, or visual perception.

Sunrise is the geometric instant at which the upper limb of the modeled solar disc first crosses above the ideal horizon. Sunset is the geometric instant at which the upper limb of the modeled solar disc completes its crossing below the ideal horizon. In this definition, atmospheric refraction is excluded: the event is calculated from Earth–Sun geometry rather than from what an observer appears to see through the atmosphere.

This convention gives every implementation the same astronomical target from the same coordinates while preserving the central principle that Ez Time belongs to geographic position, not to an individual viewing condition.

12. The Ladder Principle

Imagine a perfectly vertical one-kilometre ladder. One person stands at its foot. Another stands at the top.

Because of elevation, the two will see sunrise and sunset at different moments. The person at the top sees the Sun earlier in the morning and later in the evening.

Their Ez Time is nevertheless identical.

They occupy the same geographic footprint in the solar time model, so they occupy the same point in the solar day. Elevation does not modify the fundamental Ez Clock calculation. As long as two people share the same coordinates, they share the same Ez Time, whatever they can see.

This is not a simplification adopted for convenience. It is a statement about what Ez Clock measures: position within the solar cycle at a place on Earth, not the personal optical experience of an individual observer.

13. Consequences

Anyone standing in the Sun's path at a given latitude and longitude reads the same clock. A person in a valley, a person on a hill, a person behind a tower block, and a person in a window seat forty floors up all agree. Terrain independence and elevation independence follow from the same principle and are treated as one rule, not two.

PART IV: STRUCTURE AND NOTATION

14. Decimal Subdivision

Ez Clock abandons sexagesimal subdivision.

1 Ez Hour   = 100 Ez Minutes
1 Ez Minute = 100 Ez Seconds
1 Ez Hour   = 10,000 Ez Seconds

Each seven-hour stage therefore contains 70,000 Ez Seconds, and the complete cycle contains 210,000 Ez Seconds.

15. Notation

Format: HH:MM:SS

• HH ranges from 00 to 20 in normal display
• MM ranges from 00 to 99
• SS ranges from 00 to 99

21:00:00 is an instantaneous boundary label, not a displayable state. At the moment it would be reached, the clock reads 00:00:00. Implementations should never render a persistent hour of 21.

Examples:

16. Decimal Mathematical Meaning

Because each hour holds 100 minutes and each minute holds 100 seconds, a reading maps directly to a decimal value:

E = H + M/100 + S/10,000

So 10:50:00 = 10.5, 14:25:00 = 14.25, 17:37:50 = 17.375. Ez Clock has a naturally decimal internal structure, which makes it cheap to compute and easy to reason about.

PART V: ELASTIC TIME

17. No Fixed Physical Durations

Ez Hours, Ez Minutes, and Ez Seconds have no fixed physical duration. Each solar stage determines the duration of every unit inside it.

For a stage lasting D SI seconds:

1 Ez Hour   = D / 7
1 Ez Minute = D / 700
1 Ez Second = D / 70,000

The physical duration of Ez Time varies with latitude, longitude, date, season, solar geometry, and current stage.

18. Three Temporal Speeds

Ez Clock deliberately runs three different rates within a single day:

• Night rate, from sunset to sunrise
• Morning rate, from sunrise to solar noon
• Afternoon / Evening rate, from solar noon to sunset

One Ez Second at night may be substantially longer or shorter than one Ez Second in the morning. This is intentional. The three stages are treated as isolated temporal settings, each governed by the Sun's condition during that portion of the day.

19. Transitions Between Speeds

At 07:00:00 the clock shifts from Night rate to Morning rate. At 14:00:00 it shifts to Afternoon rate. At sunset it shifts back to Night rate.

The numerical sequence remains perfectly continuous. The physical rate changes abruptly. 06:99:99 may last noticeably longer or shorter than 07:00:00.

Ez Clock does not disguise this transition. It is information. The change of pace is the clock telling the user that they have crossed a solar boundary.

20. The Clock Should Feel Different

Ez Clock is not merely another set of numbers. Its changing speed is part of the experience. Someone watching the seconds should be able to perceive that different stages have different temporal characters. Seconds may accelerate, slow, stretch, compress, race, or move gently.

The changing rate is not noise to be engineered away. It is the language of the clock.

21. Seasonal Behaviour

Summer daylight. Longer days mean the fourteen daytime Ez Hours occupy a larger physical interval. Daytime units lengthen. Ez Time moves slowly.

Winter daylight. Shorter days compress the same fourteen Ez Hours. Daytime units shorten. Ez Time moves quickly.

Summer night. Short nights compress the seven Night Ez Hours. Night seconds are brief.

Winter night. Long nights stretch them. Night seconds are long.

22. The Clock Breathes With the Sun

During a long summer afternoon the seconds move slowly. During a short winter afternoon they fly. During a long winter night time stretches. During a short summer night it contracts.

Ez Clock is a clock that breathes with the solar cycle.

23. The Clock Dances

Time need not appear mechanically identical across every environment and season. The three stages exist in distinct temporal settings, isolated from one another, each judged by the mood of the Sun. The seconds may be understood as moving, stretching, accelerating, slowing, and dancing according to the solar day.

This is not decorative behaviour. It falls directly out of the mathematics.

PART VI: GEOGRAPHY

24. Ez Time Is Geographic, Not Political

Ez Clock has no national time zones. It does not care about national borders, regional time-zone legislation, daylight-saving laws, political boundaries, or administrative regions.

Two nearby points separated by an international border have nearly identical Ez Time. Two distant points inside one conventional time zone may differ meaningfully.

The Sun does not recognize political borders. Neither does Ez Clock.

25. No Country Setting

An Ez Clock should never ask "What country are you in?" It should determine "Where on Earth are you?" Countries are irrelevant to the astronomical calculation.

26. No Daylight-Saving Time

A government changing its clocks does not alter the Sun, Earth's rotation, sunrise, solar noon, or sunset. No adjustment is required or permitted.

27. Location Is Fundamental

A conventional timestamp can be interpreted given its time zone. An Ez timestamp is fundamentally geographic, so a formal remote timestamp should carry a geographic reference:

Ez 10:35:62 — Istanbul
Ez 10:35:62 — 41.01° N, 28.98° E

A local clock need not display its location continuously if the user already knows where the device is.

28. Continuous Location Tracking and Travel

A mobile Ez Clock derives its time continuously from the user's position. There are no time-zone boundaries to cross and no discrete jumps. Travelling from Istanbul toward London, the clock continuously recalculates solar anchors, current stage, stage duration, and the length of the Ez Hour, Minute, and Second.

There is never an instruction to "change your clock by two hours." There is a continuously evolving solar relationship, and the speed of time shifts smoothly along with it.

29. Smooth Geographic Adaptation

Position changes should produce continuously recalculated Ez Time responding to longitude, latitude, changing anchors, and fallback reference changes. Implementations should minimize arbitrary discontinuities while remaining mathematically faithful. Faithfulness outranks artificial smoothness.

PART VII: THE POLAR PROBLEM

30. The Problem

Beyond the Arctic and Antarctic Circles, a location may not experience a normal sunrise or sunset. In polar summer the Sun may never set. In polar winter it may never rise.

A literal reading of the ordinary rules would produce an Ez Day lasting weeks or months, with no daily reset and no valid anchors. Ez Clock rejects this outcome. A six-month Ez Day would be meaningless as a practical human clock: it would destroy the ordinary usefulness of hours, minutes, seconds, scheduling, and daily rhythm.

31. Solution: Nearest Valid Solar Location

If the user's position does not experience the required sunrise and sunset cycle, the clock searches outward geographically for the nearest point that does. That point becomes the temporary solar reference.

There are no national borders, no reference capitals, no political time zones, and no arbitrary cities in this search. It is purely geographic and astronomical.

32. Great-Circle Distance Rule

Let P be the user's position and V the set of all positions experiencing both required solar events on that Ez Day. The selected reference R is:

R = argmin  d(P, x)
    x ∈ V

where d is great-circle distance over Earth's surface. The rule is universal and reproducible.

33. Expanding-Circle Search

Conceptually the software draws an expanding circle around the user. The search begins at the exact location. If that point has a normal cycle, no fallback is needed. If not, the radius expands until the nearest qualifying point is found.

34. No Requirement for Land

The nearest valid point need not be inhabited, a city, a country, on land, politically recognized, or named. It may be an arbitrary coordinate over open ocean. Ez Clock follows solar geometry and does not require human settlement to validate time.

35. No Borders in Polar Mode

The search must never stop at a national border, territorial boundary, time-zone boundary, maritime border, or political jurisdiction. The solar system is continuous, so the algorithm must be continuous.

36. Anchors Under Fallback

All principal anchors derive consistently from the reference location: sunset at Ez 0, sunrise at Ez 7, solar noon at Ez 14, sunset at Ez 21/0. The polar user inherits one complete daily rhythm from the nearest place where such a rhythm naturally exists.

37. Transparency

When a substitute reference is in use, the user must be told. The fallback is never hidden.

LOCAL SOLAR CYCLE UNAVAILABLE
REFERENCE: 68.42° N, 24.17° E
DISTANCE: 143 km

The user should understand that their own coordinates currently lack a complete sunrise/sunset cycle and that the nearest valid solar reference has been selected on their behalf. Interface details remain a design question. The principle is fixed.

38. Daily Movement of the Reference

The nearest valid location moves from day to day as seasonal geometry changes. As polar summer deepens, it recedes. As conditions return toward normal, it approaches. The fallback follows the seasonal movement of the Sun.

39. Return to Local Time

The moment the user's actual location regains a valid cycle, the fallback ends. The hierarchy is simple:

1. First preference: actual geographic location
2. Fallback: nearest valid geographic solar location

40. Polar Mode Is Forced, Not Optional

The fallback is not a stylistic setting. A useful daily solar clock requires a functional daily cycle. When the local cycle becomes incomplete, Ez Clock switches automatically. This is necessary system behaviour, not a preference.

41. Why Not UTC

Using UTC or any conventional zone would contradict the philosophy. The problem is astronomical, so the solution must be astronomical. UTC describes no sunrise, no sunset, no daylight fraction, no solar noon, and no seasonal behaviour. The nearest-valid-location rule preserves the fundamental instruction: follow the Sun.

42. Travel Into and Out of Polar Conditions

Ez Clock continually evaluates position. Entering a region without a working sunrise/sunset model activates fallback. Moving nearer another valid point adapts the reference. Leaving the polar condition entirely resumes local calculation. The user's movement is part of the astronomical calculation.

PART VIII: HUMAN MEANING

43. Human Time Rather Than Mechanical Time

Ez Clock distinguishes physical duration, meaning how many SI seconds have passed, from human solar position, meaning how far a person has progressed through the local solar stage. Conventional time prioritizes the first. Ez Clock prioritizes the second.

44. Duration in Ez Clock

"The meeting lasts one Ez Hour" means exactly one current Ez Hour. It does not mean 60 conventional minutes, 3,600 SI seconds, or any fixed physical span. "60 Ez Minutes" means sixty hundredths of the current Ez Hour. Its physical length depends on the stage. This is intentional.

45. Ez Seconds Are Not SI Seconds

An SI second is an invariant physical measurement. An Ez Second is 1/70,000 of the current solar stage.

1 Ez Second ≠ constant physical duration
70,000 Ez Seconds = 1 solar stage

This distinction is fundamental.

46. Respect for Daylight Time

Ez Clock treats daylight as a finite seasonal resource. A meeting, journey, task, or interruption does not consume abstract minutes. It consumes a fraction of someone's available solar day.

One Ez Hour always represents one seventh of a solar stage, regardless of how many SI minutes that requires. One hour in winter kills far more of a person's daylight than one hour in summer. The clock makes that scarcity visible, and the sessions themselves change speed accordingly.

This creates a different social understanding of time. People should know that asking for an hour of someone's daylight in December is a larger request than asking for one in June, and the clock says so without anyone having to argue the point.

47. Seasonal Value of Time

Two one-hour daytime meetings, one in summer and one in winter, occupy different numbers of SI minutes but consume the same one seventh of their respective stages. Ez Clock measures temporal commitments against the environmental day rather than against atomic duration alone.

48. The Meaning of the Clock Face

At a glance:

The position of the number itself carries environmental meaning.

49. Avoiding the "Day Is Already Gone" Effect

Conventional time creates a disconnect from daylight. A person sees 17:00 without intuitively knowing how much usable sun remains, then looks outside and finds the day already finished.

Ez Clock exposes that information continuously. At Ez 20 the user knows immediately that daylight is nearly over. At Ez 15 they know the Sun has only recently passed maximum. Nobody should look up and think "the day is finished and I did nothing." The approach of sunset was on the clock the entire time.

50. The Sun Moves on the Watch

A central experiential goal: the movement of the Sun becomes perceptible through the movement of the clock. Watching it should convey how quickly the current stage is passing, how much daylight remains, how much night remains, whether solar noon is near, whether sunset is near, and how the season is setting the tempo.

The Sun effectively moves on the user's wrist.

51. Temporal Character

Night may feel broad and slow. A short winter morning moves rapidly. A long summer afternoon unfolds gradually. These are not subjective effects applied artificially. They emerge from astronomical duration. The Sun determines the mood of the clock.

PART IX: COMMUNICATION AND SCHEDULING

52. No Universal Ez Time

There is intentionally no worldwide Ez Time equivalent to UTC. Ez Time is local by definition, and a universal value would undermine the system. When a single simultaneous instant must be specified, conventional timestamps remain available. Ez Clock solves a different problem.

53. Ez Time and Simultaneity

Two people in different places may both experience Ez 10:00 at different physical instants. Equal Ez Time means comparable solar position, not simultaneity. This is a fundamental distinction.

54. Solar-Relative Scheduling

When two people agree to meet at Ez 10, both understand instantly where the Sun sits for the other. Ez 10 always lies between sunrise and solar noon, so both know the solar character of the appointment: how much morning is left, how far from noon, how far from dark.

This carries information that a shared UTC instant does not. Agreeing on "Ez 10 at your location" describes how far each person is through their own solar day.

55. Remote Meeting Interpretation

Someone in Istanbul and someone in Tokyo may agree: "Let's meet when each of us is at Ez 10." The meetings do not occur simultaneously, but both are at corresponding stages of their local morning.

If simultaneity is required instead, one participant's location is specified:

Ez 10 Istanbul

and the other clock converts. Ez Clock supports both solar-relative scheduling and exact cross-location conversion.

56. Conversion Between Locations

Given source coordinates, target coordinates, a source Ez timestamp, and the astronomical date, software determines the corresponding physical instant and then computes the target's Ez Time at that instant. So Ez 10:00 Istanbul might correspond to Ez 15:xx Tokyo for the same physical moment, depending on solar conditions.

57. Time Has Context

Conventional 17:00 does not tell the observer whether sunset is hours away, occurring, or long past. Ez 20:00 immediately communicates that daylight is ending. The contextual information is built into the number.

58. The End of the Day Becomes Visible

Watching the clock progress 18 → 19 → 20 → 21, the user perceives sunset approaching numerically. The end of daylight never arrives unexpectedly.

PART X: MATHEMATICS

59. Core Equations

Let:

• S₀ = first sunset
• R = sunrise
• N = solar noon
• S₁ = following sunset

Stage durations:

D₁ = R  − S₀     (Night)
D₂ = N  − R      (Morning)
D₃ = S₁ − N      (Afternoon / Evening)

For each stage i:

1 Ez Hour   = Dᵢ / 7
1 Ez Minute = Dᵢ / 700
1 Ez Second = Dᵢ / 70,000

60. Time Mapping, Night

For S₀ ≤ t < R:

E = 7 · ( (t − S₀) / (R − S₀) )        0 ≤ E < 7

61. Time Mapping, Morning

For R ≤ t < N:

E = 7 + 7 · ( (t − R) / (N − R) )      7 ≤ E < 14

62. Time Mapping, Afternoon / Evening

For N ≤ t < S₁:

E = 14 + 7 · ( (t − N) / (S₁ − N) )    14 ≤ E < 21

At S₁, E = 21 ≡ 0 and the cycle restarts.

63. Conversion to Display Notation

H = floor(E)
M = floor( 100 · (E − H) )
S = floor( 100 · ( 100 · (E − H) − M ) )

Displayed as HH:MM:SS.

PART XI: IMPLEMENTATION

64. Geographic Input

A functioning Ez Clock requires latitude, longitude, an internal astronomical date and time, and an Earth/Sun ephemeris or equivalent solar model. The user need not understand or enter any time-zone information.

65. Digital Clock Algorithm

1. Determine location.
2. Calculate solar anchors.
3. Determine whether local sunrise and sunset exist for this cycle.
4. If not, locate the nearest valid solar reference by great-circle distance.
5. Determine the current solar stage.
6. Calculate the fraction of that stage elapsed.
7. Map the fraction onto seven Ez Hours.
8. Convert to decimal Ez notation.
9. Display continuously, at the stage's own rate.

66. Physical Watch Behaviour

A physical Ez Watch is an unusual engineering problem because its second hand cannot move at a constant rate. Within each stage its speed must correspond to 10,000 Ez Seconds per Ez Hour duration, and at sunrise, solar noon, and sunset that rate changes.

An electronic watch can adjust display timing algorithmically. A mechanical implementation would require a variable-rate mechanism or continuously adjustable transmission. Such a device would physically embody the philosophy.

67. Location Permission

A portable Ez Clock benefits from device location access. Without it, the user may enter coordinates manually. A fixed household or architectural Ez Clock may be permanently configured for one coordinate.

68. Privacy-Compatible Implementation

Ez Clock does not inherently require a remote server to know the user's location. Solar calculations can be performed entirely on-device. Therefore coordinates can stay local, no national time service is needed, and no central Ez Clock authority is required.

69. Istanbul as Development Reference

Istanbul is the initial example city used to develop and test the system. This does not make it a universal origin. There is no Greenwich in Ez Clock. Every location calculates its own solar-relative time.

Reference Display Concept — Non-Normative

The following describes one practical way to present Ez Clock. These features belong to a reference implementation and do not alter the core timekeeping rules.

The 21-Division Dial

An analogue or graphical Ez dial may contain 21 principal hour divisions arranged into three equal arcs of seven. The three arcs correspond to Night, Morning, and Afternoon / Evening. Each occupies exactly one third of the dial.

The hand moves at a constant angular rate within a stage and changes rate at each solar anchor. That change of pace is meaningful information. Smoothing it away would conceal one of the system's defining properties.

A digital readout uses HH:MM:SS, with hours 00–20 and minutes and seconds 00–99. Thus 13:99:99 is the final displayed instant before solar noon and the next value is 14:00:00.

Pace Indicator

A digital implementation may optionally show the current physical duration of one Ez Second, for example:

CURRENT EZ SECOND: 0.412 SI s

This makes the current temporal rate directly visible. A longer value indicates that the present solar stage is stretched; a shorter value indicates that it is compressed.

The pace indicator is informative rather than normative: an Ez Clock remains valid without displaying it.

Solar Visualization

A reference interface may also display solar altitude, solar azimuth, a Sun-disc diagram, or a mathematically derived gnomon shadow. Such elements provide a visual check that the displayed Ez Time and the astronomical model describe the same solar state.

These visualizations are supporting evidence and interface features. They are not part of the definition of an Ez Hour, Ez Minute, or Ez Second.

Current Web Demonstrator

A web implementation may calculate Ez Time entirely on the user's device from a geographic coordinate and the device's physical clock. No central Ez time server is required.

Location can be supplied by exact device positioning, manually entered coordinates, a selected city, or another clearly labelled approximation. Exact position should not be inferred when only an approximate location is available.

A privacy-oriented implementation can keep the user's coordinates and solar calculations on-device. Optional external map tiles or geocoding services, if used by an interface, are separate from the Ez Clock calculation itself and should be disclosed as such.

PART XII: APPLICATIONS

70. Architectural Interpretation

Architecture depends deeply on solar conditions: morning Sun, solar noon, afternoon exposure, shading, glare, solar gain, seasonal daylight, façade orientation.

Instead of "this façade receives direct Sun from 08:30 until 14:15 civil time," an architect could describe exposure in Ez Time relative to the solar stage, retaining an intuitive relationship with seasonal solar position across the whole year rather than for one date.

71. Human Rhythm

Rather than every hour being mechanically identical, the clock shows whether the current stage is abundant, compressed, nearly finished, or only beginning. This encourages awareness of the limited nature of daylight.

72. Temporal Awareness

A glance communicates which stage the user occupies, how fast it is passing, how much remains, and how the season is shaping it. The clock is a scheduler and a form of environmental awareness at once.

PART XIII: COMPARISON

PART XIV: CONSTANTS AND RULES

73. System Constants, Version 0.4

21       Ez Hours per cycle
3        solar stages
7        Ez Hours per stage
100      Ez Minutes per Ez Hour
100      Ez Seconds per Ez Minute
10,000   Ez Seconds per Ez Hour
70,000   Ez Seconds per solar stage
210,000  Ez Seconds per complete cycle

Astronomical anchors:

Sunset      = 00:00:00
Sunrise     = 07:00:00
Solar Noon  = 14:00:00
Sunset      = 21:00:00 ≡ 00:00:00

74. Established Geographic Rules

1. Time is based on latitude and longitude.
2. National borders are irrelevant.
3. Conventional time zones are irrelevant.
4. Daylight-saving time is irrelevant.
5. Local buildings and terrain are irrelevant.
6. Observer elevation does not alter the core clock.
7. Sunrise and sunset are calculated mathematically from solar angle.
8. Two observers at the same coordinates share the same Ez Time regardless of what they can see.
9. The user's own coordinates are always preferred.
10. If the local solar cycle is incomplete, the nearest valid solar location is used.
11. The fallback is determined by minimum great-circle distance.
12. The fallback point may be anywhere on Earth, including ocean.
13. The fallback must be disclosed to the user.
14. Moving users receive continuously recalculated Ez Time.

75. Established Temporal Rules

1. Three distinct temporal speeds are intentional.
2. Night, morning, and afternoon/evening are independent solar stages.
3. Each stage contains exactly seven Ez Hours.
4. Each stage contains exactly 70,000 Ez Seconds.
5. Ez Seconds may differ in physical length between stages.
6. Ez Seconds may differ in physical length between seasons.
7. Ez Seconds may differ in physical length between locations.
8. Speed changes at solar anchors are intentional and unsmoothed.
9. The clock does not conceal meaningful solar transitions.
10. Duration in Ez units is solar-relative, never SI-relative.
11. The clock and the calendar are separate systems.

76. Established Human Principles

• Daylight has value.
• A short winter day and a long summer day are not identical temporal resources.
• Scheduling consumes part of a person's solar environment.
• The clock should communicate the progress of that environment.
• A user should know where the Sun is without looking outside.
• The end of daylight should become progressively evident through the clock.
• Temporal speed itself carries information.
• Time can be experienced rather than merely counted.

GLOSSARY

PART XV: DEFINITIONS

77. Short Technical Definition

Ez Clock is a 21-hour, geographically local, solar-relative timekeeping system consisting of three seven-hour stages: sunset to sunrise, sunrise to solar noon, and solar noon to sunset. Each Ez Hour contains 100 Ez Minutes and each Ez Minute contains 100 Ez Seconds. Each stage always contains 70,000 Ez Seconds, so the physical duration of Ez units expands or contracts with local solar geometry. Where a location lacks a complete daily sunrise/sunset cycle, Ez Clock adopts the geographically nearest point possessing both events, by minimum great-circle distance.

78. Short Human Definition

Ez Clock tells you where you are in the Sun's day, rather than how many fixed seconds have passed since midnight.

79. Philosophical Definition

Conventional clocks say: the unit is fixed, and nature may arrive early or late.

Ez Clock says: the Sun is the reference, and the unit may stretch or contract.

80. The Fundamental Inversion

Under conventional time, the Sun moves through the clock. Under Ez Clock, the clock moves with the Sun.

This inversion defines the entire system.

PART XVI: STATUS

81. Resolved in Version 0.4

• 21-hour cycle, three seven-hour stages
• decimal minutes and seconds
• variable hours, minutes, and seconds
• sunrise, sunset, and solar noon as anchors
• astronomical rather than visual horizon
• solar-angle definition of sunrise and sunset
• terrain independence
• elevation independence and the ladder principle
• geographic rather than political time
• continuous travel recalculation
• deliberate temporal speed transitions
• seasonally changing duration
• meeting-duration philosophy and daylight as a resource
• polar day and polar night
• nearest-valid-location fallback, forced not optional
• great-circle selection rule
• fallback transparency requirement
• separation of clock from calendar
• display range and the status of hour 21

82. Remaining Engineering Questions

The conceptual architecture is established. Remaining work is technical.

• exact astronomical model and ephemeris used
• numerical precision and floating-point rounding
• degenerate stage durations near the polar boundary. The nearest valid solar point in deep polar summer lies close to the circle boundary, where the night stage may last only minutes of physical time. The clock would then run 70,000 Ez Seconds through Stage I at extreme speed. The fallback rule as defined is correct and stands. Whether implementations should additionally require a minimum stage duration, or search for the nearest point whose shortest stage exceeds a threshold, is an open implementation question.
• GPS accuracy and update frequency during travel
• display conventions and analogue dial design
• physical watch mechanism
• battery-efficient location handling
• cross-location conversion protocol
• terminology for the three stages
• interface design for polar fallback
• a standardized format for formal Ez timestamps
• software reference implementation

None of these require changes to the fundamental philosophy.

83. Design Objective

A successful Ez Clock lets a person look and intuitively understand:

Where is the Sun in my day?

and, through its speed:

How quickly is this part of my day passing?

The system succeeds when sunset is no longer an unexpected event disconnected from the clock. The progression toward it should have been visible on the watch all day.

84. Final Principle

Ez Clock is built on the idea that human time can remain mathematically precise without being environmentally indifferent.

Its seconds need not all be identical. Its hours need not all last the same. Its days need not follow inherited conventions.

What remains constant is the structure:

0      Sunset
7      Sunrise
14     Solar Noon
21 / 0 Sunset

Everything between those points is allowed to expand, contract, accelerate, and slow according to the Sun.

Ez Clock does not ask the Sun what time it is. Ez Clock lets the Sun define time.

PART XVII: THE REFERENCE IMPLEMENTATION

Parts I to XVI define the system. This part describes ez.sy, the reference implementation, and answers the final item of §82. Everything here is a statement about this particular software, not about Ez Clock. Another implementation may differ in all of it and still be a correct Ez Clock.

85. Solar Model

Solar positions use the NOAA Solar Calculator, which implements the low-precision equations from Jean Meeus, Astronomical Algorithms. Accuracy is well under a minute at the latitudes this clock concerns itself with. Sunrise and sunset use a zenith of 90.833°, accounting for standard atmospheric refraction of roughly 34 arcminutes together with the Sun's apparent radius. This satisfies §64 and settles the first item of §82 for this implementation only.

86. Reading the Dial

The dial carries 21 divisions and one hand. Per §19, the hand moves at a constant angular rate within a stage and changes rate at each anchor. It is positioned directly and never eased between frames, because smoothing that change would conceal the one thing §19 requires the dial to show.

The ring is rotated 210° from the conventional orientation, which places solar noon exactly at the horizontal:

The three coloured arcs are the stages, each exactly one third of the circle. This is §5 made visible: numerically equal, physically unequal. The active stage is highlighted, and an inner arc shows the fraction of it already spent.

87. The Pace Indicator

Beneath the readout, the current physical length of one Ez Second is reported in milliseconds. The accompanying bar shows the current stage duration measured against an even third of the cycle, filling to the right when time is stretched and to the left when it is compressed. This states §17 and §45 as a number rather than leaving them to be inferred from the motion.

88. The Sun Disc

A circular side elevation of the sky at the active coordinates. The stick is a gnomon and the shadow is the one it casts at that instant. Shadow length is the true cotangent of solar altitude, clamped only so that a very low Sun does not run the drawing past the rim. The Sun's height on its orbit is its altitude, and the side it occupies is its azimuth.

It exists as evidence. A dial and a readout could in principle animate anything at all, but the shadow is derived from the same solar figures, so if the shadow is right the clock is right.

89. Determining Position

In order of preference:

1. A coordinate in the URL: ?city=Damascus or ?lat=33.51&lon=36.28
2. A choice made on a previous visit
3. Automatic detection from the browser's IANA time zone. A zone name is a place name, so Europe/Istanbul resolves directly to Istanbul's coordinates. For a zone absent from the table, longitude follows from the zone's current UTC offset at fifteen degrees per hour, with a coarse per-continent latitude. This costs no permission prompt and no network request, and the page labels the result as approximate. It does not violate §25: the zone is used as a geographic hint and then discarded, never as a basis for the calculation.
4. Istanbul, per §69, marked as a default

The visitor may override at any time. Use my location requests a real device fix; per §67 this is never requested automatically, since a permission prompt on arrival is hostile and usually refused. Choose a city selects from the built-in table. Pick on a map drops a pin anywhere on Earth, which is the plainest available expression of §34: no city required and no land required. Enter coordinates accepts decimal degrees with an optional hemisphere letter in either order.

90. Polar Fallback in Practice

Implementing §32 literally would mean searching a continuous surface. Because validity depends on latitude once longitude is fixed, the nearest valid point on the meridian through the observer is found by walking toward the equator in half-degree steps until a valid latitude appears, then bisecting to refine it. The substitute coordinates and the great-circle distance to them are displayed and never hidden, per §37.

91. Privacy

§68 is met literally. There is no backend, no account, no geocoding service and no analytics on position. Every calculation runs in the browser from a coordinate and the device's own clock. The visitor's choice is stored in local storage on their own machine.

One exception, stated plainly: the map panel requests tile images from OpenStreetMap when opened, which reveals the area being viewed to that service in the way any map does. The coordinate box does the same job with no network involved.

92. Theme and Mode

Two independent axes. Theme is a place: eleven cities, each with its own palette and type. Consistent with §24, choosing Tokyo changes how the page looks and nothing else. It does not move the visitor there and never touches the calculation. Mode is a light level, offered as system, light or dark from the header. System follows the operating system and keeps following it while the page is open.

93. Construction

A static site. Every display is written from a single reading per clock per frame, so the dial, the digital readout and the shadow cannot drift apart: they are three views of one number. Once the shell is cached the clock runs permanently offline, because there is no time service to call and nothing to fetch. A coordinate and the device clock are sufficient, which is §68 carried to its conclusion. The only things needing a network are the first visit and the map.