Space & Cosmos · Project 4 of 12

The Prayer-Time Error

How many minutes wrong the prayer timetable is

Time the sunset from your own doorstep for fourteen evenings and find how many minutes your timetable is out.

The calendar this needs: Twenty-eight dusk observations in all — fourteen consecutive evenings for the baseline, then fourteen more against the corrected table — so the baseline must start in week one and the second fortnight cannot begin until the corrected sheet has been approved and handed out.

Six weeksNo equipment on the paper route 20 written stepsMarked out of 20Free forever
The question

How many minutes does the printed or app timetable differ from the event you actually see from one fixed spot, and where does that difference come from?

A published time is the output of a model, and the moment you see is an observation; the gap between the two is exactly what positional astronomy exists to account for. Surveyors, satellite operators, flight planners and anybody who publishes an almanac are paid to know the size of that gap, its causes and its limits. The method here is theirs: fix a station, synchronise a clock, observe repeatedly, and report the residual with its spread instead of one confident number.

Two acts. Find, then fix.

Every EAD project runs the same shape. The first act produces a number nobody in the room could previously state. The second act changes exactly one thing and proves whether that number moved.

Act 1 · Find
You stand on one marked spot for fourteen evenings and record, to the minute against a clock synchronised to network time, the moment the sun leaves your horizon. You set that observation against what the wall calendar says, what the app says, and what an astronomical computation says for your exact coordinates.

A one-page costed problem statement carrying four lines: whose problem this is, the mean signed difference in minutes at this spot, the worst evening in the fortnight, and a modelled yearly total of mistiming across the counted people who use that same table here, labelled as modelled and carrying the count it rests on. Beside it sits a chart of the signed difference against date with a line at zero, the source and stated location of every published time, the error budget of your own method in minutes, and one line stating that this is an observation of visibility from one spot and not a religious ruling.

Act 2 · Fix
You publish a corrected table for that one spot, built by applying your measured offset to the computed times, with its evidence and its limits printed on the same page. You then put it in the hands of at least five adults, logged as U1 to U5 rather than by name, observe fourteen more evenings against it, and count use in user-days recorded by the users themselves.

The residual difference in minutes between the corrected table and fourteen fresh observations, the adoption count in user-days backed by tick sheets or message threads rather than memory, and every user's answer to the same two questions written word for word against their code, including the answers of those who stopped.

What actually gets measured

The numberminutes between the published time and the event observed from one fixed spot, in minutes, signed as observed minus published, printed with its error budget — the minutes your eye, your clock and your blocked horizon each contribute — beside it
BeforeFourteen consecutive evenings observed from one chalk-marked spot at one marked eye height, each read to the minute from a clock checked against network time, subtracted from the printed calendar time, the app time and the computed time for the same date. Reported as a mean with its largest and smallest value, cloudy evenings marked unusable rather than filled in.
AfterFourteen further evenings observed from the identical spot, at the identical eye height, with the identical clock check, subtracted from the corrected table you published. Reported the same way, alongside the count of user-days recorded by the five or more users, logged as U1 to U5.
The honest partA well-measured failure scores higher than an unmeasured success. If the number did not move, say so and explain why.

If your household cannot run this

The whole method runs on school property with a member of staff. The school fixes one ground-level spot in the yard with a clear western edge, keeps the chalk mark and the eye-height card between sessions, and a named member of staff stands with the learner for each dusk observation. The school clock is the reference, the school holds the corrected sheet, and staff hand it to the users. This is for any learner with no clear horizon, no safe spot, no watch they can set, or no household that can take part. It is marked against the same twenty points as every other version, and it is not a reduced one.

Every step, written out

Twenty steps in total — ten to find the number, ten to fix it. Pick the route that matches what your school actually has.

A chalk mark, a watch set from a known-accurate clock and a ruled notebook produce the same minutes figure; the published times come from the calendar on the wall and a newspaper, and each source is written down with the place it was computed for.
You need: One fixed observation spot at ground level, never a roof or a parapet, marked with chalk on the floor, with a card taped at eye height on the frame beside it · A watch or clock with a second hand, set from a known-accurate clock and re-checked against it every third evening · The wall calendar or printed timetable, kept undamaged, plus a newspaper carrying the same daily times as a second published source · A notebook ruled into seven columns: date, calendar time, second source, observed time, difference, sky, notes · Squared paper, a ruler and a pencil for the fourteen-day difference chart drawn to a stated scale · A sheet of paper pinned where people pass, carrying the corrected table copied out by hand

  1. Fix the spot

    45 minutes
    Choose one spot you can stand on every evening for a month and fix it so it never moves.
    • Choose a spot at ground level with a view of the western skyline — a ground-floor window or doorway, a yard, a school ground. Never a roof, a parapet, a balcony rail or anywhere you would have to climb.
    • Name in the notebook the adult who will stand at the spot with you for every observation, and a second named adult who stands in when the first cannot. Being told where you are is not enough; the named adult is there.
    • Mark the standing position with chalk and tape a card at your eye height on the frame beside you, so height as well as position is fixed.
    • Draw the western skyline on the first page of the notebook and mark on it the wall top, ridge or roof line the sun goes behind.
    • Pace out and write down where the spot sits: which room, which side of the building, how many steps from a named door.
    • Write one line on what blocks the true horizon and roughly how high it stands above your eye height.
    Write down: The description of the ground-level spot, the two named adults who will stand there with you, the eye-height mark, the paced position, and the drawing of the skyline with the blocking edge marked.
    Finished when: Another person can find the chalk mark from your written description alone and see the skyline you drew.
    Commonest mistake: Stepping half a metre aside because the view is better. A different standing point puts a different edge in the way and moves the moment of disappearance; mark the spot and keep it.

  2. Prove the clock

    30 minutes, plus 5 minutes every third evening across both fortnights
    Set your watch from a clock known to be accurate and record how far it drifts.
    • Find a clock known to be accurate — one set from a network, a radio time signal, a station clock or a television news clock — and name it in the notebook.
    • Set the watch against it to the second, and write the date, the time and the clock you used.
    • Re-check the watch against that same clock every third evening and write the drift in seconds each time, including the zeros.
    • Write your error budget on the same page before you start: how many seconds the watch drifts between checks, how many seconds you lose deciding the moment the light goes, and how coarse the horizon edge is. Add them up and carry that figure beside every minutes result you report.
    • Agree the rules aloud with the named adult who will stand with you: which ground-level spot, which time, and that you never look at the sun or through any lens.
    Write down: The reference clock named, the setting time and date, the drift in seconds at every third-evening check, and the three-part error budget in minutes.
    Finished when: The notebook holds at least five dated drift readings, the watch has never been more than a minute from the reference, and the error budget is written where you can copy it onto every result.
    Commonest mistake: Setting the watch once and trusting it for a month. Write the drift down; a watch that slips two minutes turns a real finding into a wrong one.

  3. Read the tables

    50 minutes
    Copy out what the calendar and a second published source state for your fourteen dates.
    • Copy the wall calendar or printed timetable times for the next fourteen dates into the first column, exactly as printed.
    • Find a second published source — a newspaper's daily times, a mosque notice, a second printed calendar — and copy its times for the same dates.
    • Write down which city, zone or point each source says it was computed for; where it does not say, write 'not stated'.
    • Write where each source came from and on what date you copied it, so the copy can be traced back.
    • Rule the remaining columns for observed time, difference in minutes, sky condition and notes.
    Write down: Fourteen dated rows carrying two published times each, with the name, source and stated location beside every one.
    Finished when: All fourteen dates carry two published times and both sources are named on the page with the date they were copied.
    Commonest mistake: Copying only one source because the second is hard to find. The gap between two published tables is a finding on its own, and it costs one walk to get it.

  4. Watch fourteen evenings

    20 minutes each evening for fourteen evenings
    Observe the actual moment from the fixed spot for fourteen evenings and record it to the minute.
    • Stand on the chalk mark ten minutes early, at ground level, with one of your named adults standing there with you for the whole observation. If neither can come, the evening is not observed.
    • Keep your eyes on the wall top, ridge or horizon edge and never on the disc itself, and use no glasses, binoculars, camera or lens of any kind.
    • Note the minute the last light leaves that edge, reading the watch you set in step two.
    • Write the reading in the notebook while still standing on the mark, before you move.
    • Record the sky in three words, and mark any evening you could not see the edge as unusable rather than guessing.
    Write down: Fourteen dated observed times to the minute, which named adult stood with you each evening, the sky condition for each, and a clear mark against every evening lost to weather.
    Finished when: At least ten usable evenings carry an observed time with an adult named beside it, and every unusable evening is written down as unusable rather than left blank.
    Commonest mistake: Filling in a cloudy evening from the calendar so the row looks complete. A missing observation is data; an invented one destroys the whole table.

  5. Work out the error

    55 minutes
    Calculate the signed difference in minutes against both published sources and describe how it behaves.
    • Subtract the calendar time from the observed time for every usable date, longhand in the margin, keeping the sign so early and late stay apart.
    • Repeat against the second published source, filling the second difference column on the same rows.
    • Add the differences and divide by the number of usable evenings, longhand, then underline the largest and the smallest.
    • Draw the fortnight on squared paper: difference in minutes up the side, date along the bottom, a ruled line at zero, and the scale stated.
    • Copy your error budget from step two beside the mean, and state plainly what it means: a mean smaller than the budget is not a finding you can claim, only a limit you can report.
    • Look along the chart and write one line: does the difference sit level across the fortnight, or does it climb or fall from the first evening to the last. That answer decides what the corrected table is allowed to cover.
    • Write one plain paragraph on why an error exists at all: the table is computed for a city centre or a broad zone, while you stand at your own longitude, your own altitude and behind your own wall, and a wall or a hill changes the moment the sun disappears from where you are standing.
    Write down: Two columns of signed differences, the mean and the range for each source with the error budget printed beside it, the drawn chart, the paragraph explaining the cause, and the one-line verdict on drift.
    Finished when: You can state the mean difference in minutes for your spot, with the error budget beside it, and say in one written line whether it holds steady across the fortnight or drifts.
    Commonest mistake: Dropping the signs and averaging the sizes. Three minutes early and three minutes late average to zero, not to three, and the direction is the whole finding.

  6. Name the cost

    50 minutes
    Finish the costed problem statement and commit to publishing a corrected table for this one spot.
    • Write four lines: whose problem this is, the mean difference in minutes at this spot with its error budget, the worst evening of the fortnight, and the minutes of mistiming per person per year at that mean — marked as an annualised figure that assumes this fortnight is typical, which it may not be, because the sun sets against a different part of your skyline in December than in June.
    • Count the people who use the same table at or near this spot, write the count down, and multiply longhand to get a total in person-minutes a year. Label it plainly on the page: this is a modelled figure resting on a count of [number] people and one fortnight of observation. It is not money, it is not time anyone lost, and nobody has been asked whether the minutes mattered to them.
    • Write one line without hedging: this measures visibility from one spot, it is an observation and not a verdict, and questions of religious practice belong to a qualified scholar.
    • Choose the fix and write it as one sentence: 'I will publish a corrected table for this spot and get at least five people to use it for fourteen days.'
    • Read the page aloud to an adult in the household and write their reaction down in their own words.
    Write down: The one-page costed problem statement, the counted people and the modelled person-minutes marked as modelled, the sentence about the scholar, and the fix as one testable sentence.
    Finished when: Somebody who was not there reads the page once and repeats both your minutes figure and the sentence about the scholar back correctly.
    Commonest mistake: Writing the page as a claim about what is correct to do. The page reports what was seen from one spot on fourteen evenings; that is the only claim it can carry.

  7. Build the table

    60 minutes, plus the wait for your teacher to approve the sheet
    Write out a corrected table by hand, covering only the dates your evidence covers, with its evidence and its limits printed on it.
    • Take the drift answer from step five first. If the offset held level across the fortnight, you may write a table for the dates immediately around it. If it climbed or fell, you may not extend the offset forward at all: correct only the dates you observed, and say on the page why the rest are missing.
    • Print the valid-from and valid-to dates in the largest type on the sheet. The sun's setting point moves along your skyline through the year, so a wall or a ridge gives a different offset in a different month, and a table used past its dates is wrong in a way the reader cannot see.
    • Copy the printed source's times for those dates into a fresh ruled page, one date per line, add your measured mean offset longhand, and write both the original and the corrected time so the arithmetic stays visible.
    • Write a header block: the exact spot, how to find it, the dates observed, the mean offset, the range, the error budget in minutes and the number of usable evenings behind it.
    • Write a footer block: the horizon this table assumes, the plain statement that it does not hold for anyone standing elsewhere or on any date outside the printed range, and the sentence that this is an observation and not a verdict, and that questions of religious practice belong to a qualified scholar.
    • Give the finished sheet to your teacher and get the sheet and its wording approved and initialled before a single copy leaves you. Nothing is handed to anyone until that initial is on it.
    • Where the table is going beyond your own household, your school writes to the community first — the mosque, the committee or the notice-board keeper — and the copies go out only after that reply. A learner does not introduce a corrected timetable to a community on their own.
    • Give an approved copy to one person who was not involved, ask them what it means, and correct anything they misread, then have the correction initialled again.
    Write down: The corrected table with both times per row, its valid-from and valid-to dates, its header block, its footer block, your teacher's initial and date, any reply from the community your school wrote to, and a note of what the first reader misunderstood.
    Finished when: The table fits on one page, states its offset, its error budget, its evidence and the dates it is valid for, carries your teacher's initial, and a stranger can say what it is for and what it is not for.
    Commonest mistake: Publishing a rounded offset with no range beside it. Write the mean and the spread together, so a reader knows how tightly to trust it.

  8. Find five users

    45 minutes
    Put the corrected table in the hands of at least five people and agree how their use will be recorded.
    • Copy the approved table out five times by hand or at a print shop, and give one to each of five adults who stand at or near your spot.
    • Explain the one number and its limits in under a minute to each of them, and ask directly whether they will use it for the dates the table is valid for.
    • Tell each of them, in the same breath, that they can stop at any point without giving a reason, and that stopping is written down as a result and never as a failure.
    • Write the answer down, including every refusal, and agree how use gets recorded: a tick sheet pinned beside the table, or one question you ask at a fixed time.
    • Write the user ledger in codes: U1 to U5, each with a role, the date given, the recording method agreed and their first reaction word for word. No names go in the ledger. The sheet matching codes to people is held by your school and destroyed after moderation.
    • Write your expected adoption on a page, date it, and have one person sign as witness before the fortnight starts.
    Write down: The coded user ledger, U1 to U5, with role, date, recording method and first reaction, the sentence telling each user they may stop at any time, and the witnessed dated prediction.
    Finished when: Five coded users hold a copy, each has told you on the record whether they intend to use it, and each has been told they may stop without a reason.
    Commonest mistake: Handing out ten copies and calling it ten users. A copy given is not a use; the count rises only when somebody records using it.

  9. Measure the fortnight

    20 minutes each evening for fourteen evenings, plus 45 minutes
    Observe fourteen more evenings against the corrected table and count who actually used it.
    • Observe from the same ground-level chalk mark at the same eye height, with a named adult standing there with you, under the same safety rules, recording the observed minute exactly as before.
    • Subtract the corrected table time from the observed time each evening, longhand, to get the residual error in minutes.
    • Collect every user's tick sheet on the agreed day and count days ticked, not copies handed out.
    • Ask every user the same two questions and write the answers word for word against their code, U1 to U5: did it change what you did, and will you keep using it.
    • Write down every reason a user stopped: forgot, did not trust it, moved away, disagreed with the idea, or gave no reason at all, which they are entitled to do.
    Write down: Fourteen residual differences with the error budget beside the mean, the adoption count in user-days, and every coded user's recorded answers including those who stopped.
    Finished when: You can state the residual error in minutes with its error budget and the number of user-days, and both rest on records other people made.
    Commonest mistake: Counting a user who says they used it with nothing written down. Ask for the tick sheet; memory inflates adoption every time.

  10. Share and reflect

    60 minutes
    Publish the finding, defend it to real people, and record what happens to the table now.
    • Answer ten to twelve minutes of unseen questions live, in front of two witnesses who sign and date the page: the spot, the clock evidence, the mean error, the error budget, the corrected table and its valid dates, the residual, the user-days and the limits. On this route there is no recording at all.
    • Read the one-page explainer to three people who use the table and write down what each of them said.
    • Hand or send the drawn chart to the expert your teacher approached, with one question: what would you have measured that I did not.
    • Ask the coded users in front of a witness whether the table stays on the wall and why, and write the answers word for word against their codes.
    • Complete the relations ledger with ten codes, roles, dates and what each person replied.
    Write down: The defence, signed and dated by its two witnesses, the one-page explainer, and the coded relations ledger holding ten relationships.
    Finished when: Ten coded relationships are logged with dates and replies, and the users have said on record whether they keep the table.
    Commonest mistake: Ending on how useful people said it was. The metric is minutes and user-days — report those first and opinions second.

What the student hands in

Nine pieces. Together they are the folder a parent can sit down and read.

1. Question cardOne card naming the exact spot, its coordinates or paced description, the tables being tested, and the question: how many minutes out is this table for this doorstep, and why.
2. Expert interview packFive written questions for an astronomer, surveyor or almanac compiler, your fourteen-day difference chart attached, the date your teacher sent it and to which institution and role, and the reply recorded word for word — or, where no reply came, the dated attempts and one named published source in its place.
3. Evidence logEvery observed time with its date and sky condition, every clock check with its offset in seconds, and every published time with the source and the location it was computed for.
4. Failure logThe evenings lost to cloud, the night you arrived late, the watch that drifted, the user who stopped ticking the sheet, and what each of them did to the comparison, all dated.
5. The buildThe corrected one-page table itself, with its header of evidence, its printed valid-from and valid-to dates, its footer of limits and your teacher's dated approval, together with the two charts of signed difference: the fortnight before and the fortnight after.
6. One-page explainerOne page a neighbour reads in ninety seconds: the spot, the mean minutes, why a table computed for a zone misses a doorstep, the corrected table, and the line about the scholar.
7. Identity cardA name and a one-line promise for the corrected table, so people can refer to it by name, plus the single sentence you want repeated at somebody else's table.
8. Relations ledgerTen coded entries, each with a role, a date and what was said, and no names: E1 the astronomer or surveyor, A1 to A3 the people affected who use the table, P1 to P3 the peers who checked your arithmetic, and R1 to R3 the people your chart went to who answered. The sheet matching codes to names is held by the school and destroyed after moderation. No health, financial-hardship or literacy information about a named person is recorded anywhere in it.
9. The defenceTen to twelve minutes of unseen questions, answered live in front of two witnesses who sign and date the page: the spot, the clock evidence, the mean error with its error budget, the corrected table and the dates it is valid for, the residual, the user-days, and the limits you accept without argument. A recording is optional evidence and never the requirement; on the No-Tech route there is no recording at all.

The expert they have to find

Ten logged relationships are required before this project can be marked. One of them is an expert, and this is who.

An observational astronomer, a physics or astronomy lecturer, a land surveyor who works in coordinates, or whoever computes the times a local calendar prints. A member of an amateur astronomy society who does timing work is just as good.

How to find one

Work by institution and role, never by hunting down a named individual. The roles that fit are: a physics or astronomy department at a university, an amateur astronomy society that runs public observing nights, the meteorological department's public enquiries desk, and the surveyor's office at a municipal or revenue authority, where somebody works in coordinates every day and will explain longitude faster than anybody. The learner names the institution and the role they want. The teacher makes the approach, from a school address, and every reply comes back to that address.

What to say

Dear [name or role], I teach at [school]. One of my learners has timed sunset from one fixed spot on [number] evenings against a clock checked to the second, and the observations sit several minutes away from the printed table. Could you spare fifteen minutes — on a call with me present, or by written reply, whichever suits you? Their five questions are below.

What to ask

  • When a sunset time is published for a city, which point in that city is it computed for, and what horizon does the computation assume?
  • How many minutes can a wall, a ridge or a block of flats on the western skyline move the observed moment away from the computed one?
  • How far apart do two spots have to be, east to west, before their sunset times differ by a full minute at this latitude?
  • When you time an event by eye, what exactly do you take as the moment, and how closely do two observers usually agree?
  • If I published a corrected table for one spot, what would you insist appeared on the page before anybody used it?

If no reply comes, the learner submits the questions as they were sent, the dated record of the attempts and one named published source in the expert's place, and that route scores — the gate is never met by compelling a reply.

The defence

Eight of the twenty marks. A student who cannot answer these has not finished, however good the artefact is.

  • Would those five people have changed their timing anyway without your table, and how do you know?
  • Your horizon is blocked by a wall. How much of your offset is longitude and altitude, how much is that wall, and how would you separate the two?
  • You lost evenings to cloud. Convince me the mean you published is stable, and tell me what a second fortnight would most likely have shown.
  • Somebody carries your table two streets away and uses it. What error have you handed them, and what did you print on the page to prevent it?

How far a student can take it

starterYou observe from one marked spot on at least ten usable evenings, record each time to the minute against a checked clock, and put your questions, through your teacher, to one professional who works with time or sky.
practitionerYou choose the observation spot and defend the choice, cite the source and the stated location of every published time you compare against, and make one chart a stranger reads correctly without your help.
researcherYou write the protocol before the first evening, justify fourteen nights rather than three, and quantify in seconds the error added by your eye, your clock and your blocked horizon separately.
contributorYou set your measured offset against a published ephemeris or an observatory figure, defend your method to an astronomer who disagrees, and publish every raw observation through your school, where your school agrees it may be published, so others can recompute it.

If you want to go further

Repeat the fortnight from a second spot two hundred metres away with a different skyline, and chart the two offsets on one axis.

When it goes wrong

  • If nobody replies to your interview requests - then ask your teacher to send the same five questions to a second institution on the brokered contact list, take a written reply instead of a call, or attend a public observing night with a named adult who stays with you; and if none of that produces an answer, submit the questions as sent with the dated attempts and one named published source, which scores.
  • If your before and after look the same - then report that as the finding, check first whether the coded users actually used the table on each of the fourteen evenings, and write what you find in the failure log.
  • If you cannot see the horizon on most evenings - then choose a fixed edge you can always see from the same ground-level spot, a roof line or a wall top seen from below, define and photograph that edge, and report every time against it instead.
  • If the household or the site says no - then run the school version: one ground-level spot on school property, a member of staff standing with you, and the school's clock as the reference. It is marked the same.
  • If somebody reacts badly to your standing there or to the table - then stop, leave, and write down what happened. Then tell the adult who knows where you are, the same day, and tell your teacher before the next session.
  • If you run out of time - then shorten the second fortnight to seven evenings rather than dropping the first, and print the shortened period on the chart itself.

Before you start

Safety and consent.
  • Never look at the sun. Not with the naked eye, not through a phone or camera screen, not through glasses, sunglasses, binoculars, a telescope or any lens. Keep your eyes on the wall top, the ridge or the horizon edge and note the moment the light leaves that edge.
  • Observe from one fixed spot at ground level and nowhere else — a ground-floor window or doorway, a yard, a school ground. Never a roof, a parapet, a balcony rail or any place you would have to climb to reach. A named adult stands at the spot with you for every one of the twenty-eight evenings, not merely knowing you are out there, and a second named adult stands in when the first cannot come. If neither can be there, the evening is not observed. Never observe from an unlit street or an open plot, and never alone.
  • This project measures visibility from one spot. It is not a religious ruling. Write on every page you publish that this is an observation and not a verdict, and that questions of religious practice belong to a qualified scholar.
  • Take nothing to the observation spot that you would not want to drop: no glass, no borrowed phone held over a parapet, no chair dragged to the edge to see further. If the view needs a climb, choose a different spot.

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