Igor Barani

0h Origin

The question

Where do you measure from?

The answer

From a point that can be named and found again. Every other place gets its address from there.

  1. The sky is measured from the first point of Aries.

    BecauseThat is where the Sun crosses the celestial equator, heading north, at the March equinox. Anyone can find it again by observation, so it serves as zero.

  2. The point has left the Ram. It now lies in Pisces.

    BecauseEarth's axis turns slowly, once in about 26,000 years, and carries the equinox west along the zodiac. This turning is called precession. The point was named more than two thousand years ago, when it lay in Aries, and the name stayed.

  3. A letter is measured from the baseline.

    BecauseEvery letter in a line stands on it, so heights are counted up from there: the x-height, the cap height, the ascenders. Descenders are counted down.

  4. A radiosurgery plan is measured from a frame.

    BecauseA frame fixed to the head defines x, y and z. In the Leksell system the frame's center is set at 100, 100, 100 millimeters, so every point inside the head has a positive address.

Three zeros. The sky's, where the ecliptic crosses the celestial equator. The letter's, the baseline of Barani Sans, with its x-height, cap height and descender in units of the em. The Leksell frame's, at one corner, so that the frame's center reads 100, 100, 100 mm. Schematic.

Another way

Measure from the observer instead, by height above the horizon and compass bearing.

BecauseThat address changes every minute as the sky turns, and it differs from town to town. Atlases measure from the first point so that one address serves everyone.

Check

At the March equinox the Sun stands at the first point of Aries, so its right ascension and declination are both zero. The line on the opening page shows how high that point stands over Phoenix right now.

KeepMeasure from a point you can find again.

Igor Barani

Igor Barani designs type and figures, builds with artificial intelligence, writes about healthcare, and makes the With Every Reason mathematics books. By day he is a radiation oncologist who treats only tumors of the brain and spine, and Professor and Chairman of Radiation Oncology at Barrow Neurological Institute in Phoenix, Arizona.

A note on the chart. The star names bundled with d3-celestial, the open atlas behind this chart, list 33 Arietis as Barani. It is a faint double star in the Ram, the small ringed star northeast of Hamal. The International Astronomical Union has not adopted that name. In 2017 it gave the similar name Bharani, a lunar mansion of Hindu astronomy, to the neighboring star 41 Arietis.

Writing at 0h

1h Typography

The question

How large must the type on a slide be for the back row to read it as easily as a book?

The answer

Large enough that each letter makes the same angle at the back row as book type makes at reading distance. With the back row six screen-heights away, that is about 27-point type on a standard 16:9 slide.

  1. Measure type by the angle it makes at the eye.

    BecauseA letter twice as far away looks half as tall. The eye judges the angle, not the size on the page.

  2. Take book type as the standard: its x-height makes about 0.24° at 40 cm.

    BecauseLegge and Bigelow measured printed books and found that average. At 40 cm it is an x-height of about 1.7 mm.

  3. Carry the angle to the back row.

    BecauseSix screen-heights away, an angle of 0.24° spans 6 × tan 0.24° = 2.5% of the screen's height. The size of the hall drops out; only the ratio of distance to screen height counts.

  4. Turn the fraction into points.

    BecauseA 16:9 slide is 7.5 inches, or 540 points, tall. 2.5% of 540 is 13.6 points of x-height, and in a face whose x-height is about half its size, that is 27-point type.

  5. Treat 22 points as the floor.

    BecauseBelow an x-height of about 0.2°, reading slows even for good eyes. From six screen-heights, 0.2° is 22-point type.

The same angle at the eye. A book letter at 40 cm and a slide letter at the back row fill it equally. Not to scale.

Another way

Test the slide on a laptop. Step back to six times the height of the laptop's screen and read it from there.

BecauseThe angle depends only on distance divided by screen height, so the laptop at six heights shows what the back row will see.

Check

Work back from the answer. 27-point type has an x-height of about 13.5 points, which is 2.5% of the slide's 540. On a screen 3 meters tall that is 75 mm, and 75 mm seen from 18 meters makes 0.24°.

KeepSize type by the angle at the back row.

Type at work

Igor Barani is making a type family for the With Every Reason books. Barani Serif adapts EB Garamond, and Barani Sans adapts Hanken Grotesk, with forms that keep 1, l and I, and 0 and O, apart for children. He also sets his own slide system for scientific talks and the themes of the editor he writes code in.

Until Barani Sans is released, this site is set in Hanken Grotesk, the face it adapts, with Doto, a dot-matrix face by Óliver Lalan, for its labels.

Writing at 1h

2h Design

The question

A figure carries more ink than its data needs. What should go first?

The answer

Every mark that tells the reader nothing about the data. Delete first, and refine only what is left.

  1. Name every mark on the figure.

    BecauseA mark that has not been named cannot be judged.

  2. Ask what each mark tells the reader about the data.

    BecauseEdward Tufte called the ink that shows data the data-ink. All other ink competes with it for the eye.

  3. Delete the marks that tell nothing.

    BecauseThe box around the plot, the background grid and the drop shadows each draw the eye and carry no value.

  4. Replace the legend with labels at the ends of the lines.

    BecauseThe reader then looks once instead of twice: at the line, not at the line and then the key.

  5. Only now refine what remains: weight, spacing, alignment.

    BecauseRefining a mark that should have been deleted is wasted work.

The same two series, before and after. Nothing was added; the frame, grid, shadows, markers and legend were deleted, and the lines were labeled directly. Example data.

Another way

Build from nothing. Start with the data alone, and add a mark only when the figure fails without it.

BecauseIt is the same test run in the other direction, and it never lets clutter in.

Check

Cover each remaining mark with a finger. If the figure still says the same thing, that mark can go too.

KeepDelete first. Refine what is left.

Design at work

Igor Barani holds his figures to the standard of a Nature review: uncluttered, labeled directly, and clear when projected for a room. He prefers drawn cross-sections and labeled cutaways to stock photographs, with one exception: medical images stay real.

Writing at 2h

3h Artificial intelligence

The question

A language model drafts the next step of a worked solution. How can a wrong step be stopped before anyone reads it?

The answer

Let the model propose and let code decide. A checker that computes the result accepts the step or sends it back.

  1. Write down what a correct step must satisfy.

    BecauseA rule that is written down can be checked by a program. A rule that lives only in a prompt cannot.

  2. Have the model return the step as typed fields: the claim, its numbers, its reason.

    BecauseCode can read fields without guessing. It cannot reliably read free prose.

  3. Check every number by computing it.

    BecauseArithmetic has one right answer, and a program finds it every time. A second model would be a second guess.

  4. When a step fails, ask once more, then use the step written by hand.

    BecauseOne bounded retry keeps the lesson moving, and an unchecked step is never shown.

The model proposes; the checker decides. A step that fails twice is replaced by the step written by hand.

Another way

Have a second model review the first.

BecauseIt catches what no rule covers, such as a confusing word or a reason that does not fit. It can be wrong too, so its verdict is advice, not a gate.

Check

For 8 + 5, the model proposes “eight needs three to make ten.” The checker computes 10 − 8 = 2 and rejects the step. The step written by hand is shown instead: eight needs two.

KeepLet the model propose. Let the code decide.

Intelligence at work

Igor Barani builds multi-agent systems in Rust, with every step observable and written rules for what each agent may do. He also builds and runs the infrastructure they need.

Writing at 3h

4h With Every Reason

The question

A child writes 8 + 5 = 13 but cannot say why. What is missing?

The answer

A reason for each step. Arithmetic is a chain of small claims, and each claim rests on one the child already knows.

  1. Eight needs two to make ten.

    BecauseEight and two make ten, a pair learned earlier.

  2. Take the two from the five. Three are left.

    BecauseFive is two and three.

  3. Ten and three is thirteen.

    BecauseOne ten and three ones are written 13.

Sticks and a bundle, as in the kit. Two sticks move from the five to finish the ten.

Another way

Fill the five instead. Five needs five to make ten, so take five from the eight; three are left. Ten and three is thirteen.

BecauseThe same pairs to ten do the work from the other side.

Check

Add in the other order: 5 + 8 = 13. Or count on from eight: nine, ten, eleven, twelve, thirteen.

KeepEight needs two. Ten and three is thirteen.

With Every Reason

With Every Reason is a series of mathematics books by Igor Barani, published by KAGU, LLC, under the line “Every answer, with a reason.” Every worked solution gives each step with its reason, in the manner of Andrei Kiselev's textbooks. Each new idea opens with a problem the child's present tools cannot finish, after the method of Vasily Davydov. A kit of wooden sticks and bundles comes with the books, so that the hands do each step before a word names it.

The series is planned as 21 books, from kindergarten through grade 12. The first books, kindergarten to grade 6, are in preparation.

This site is written the same way: the question, the answer, the steps with their reasons, another way, a check, and one line to keep.

Writing at 4h

5h Healthcare

The question

A clinic is busy 90% of the time, and its patients still wait. Why do waits grow so fast as a service nears full?

The answer

Waiting grows as ρ / (1 − ρ), where ρ is the share of time the service is busy. At 90% busy, a patient waits on average nine times as long as a visit takes. At 95%, nineteen times.

  1. Measure how busy the service is.

    BecauseThe share of time someone is being seen is the arrival rate divided by the rate at which visits finish. Queueing theory calls it the utilization, ρ.

  2. Model the simplest queue: random arrivals, visits of random length, one room.

    BecauseFor that queue the average wait in line is ρ / (1 − ρ) visit-lengths, and real clinics behave like it closely enough to show the shape.

  3. Put numbers in.

    BecauseAt 80% busy the wait is 4 visit-lengths, at 90% it is 9, and at 95% it is 19.

  4. See where the cost lands.

    BecauseGoing from 90% to 95% busy uses five more points of capacity and doubles the wait. The last few points cost the most.

Average wait in line, in visit-lengths, against the share of time the service is busy. The upper curve has visits of random length; the lower one, visits of fixed length.

Another way

Make visits regular instead of adding capacity.

BecauseWhen every visit takes the same time, the wait halves to ρ / (2(1 − ρ)). At 90% busy it falls from 9 visit-lengths to 4.5, with no new room and no new staff.

Check

Simulate it. A run of 360,000 patients at 90% busy gave an average wait of 9.3 visit-lengths. With fixed visit lengths, the same run gave 4.5.

KeepThe last few points of capacity cost the most waiting.

Healthcare at work

Igor Barani writes about healthcare from inside it, as a physician who also runs a department.

Writing at 5h

6h Practice

The question

A tumor sits a few millimeters from a nerve. How can the tumor receive a lethal dose while the nerve receives almost none?

The answer

Aim beams from many directions, each too weak to harm what it crosses, and let them meet only at the tumor.

  1. Give the tumor an address.

    BecauseA point can be aimed at only after it has coordinates. A frame or a fitted mask fixes x, y and z to the head.

  2. Read the address from images.

    BecauseMRI and CT, registered to the frame, place the tumor and the nerve in the same coordinates.

  3. Aim many beams, each too weak to harm what it crosses.

    BecauseTissue along any one path receives only that beam's small share. The Gamma Knife Icon carries 192 cobalt-60 sources, in eight sectors of 24.

  4. Let the beams cross only at the tumor.

    BecauseDoses add where beams overlap. The point where all of them cross is called the isocenter, and it receives the full dose.

  5. Let the edge fall away steeply.

    BecauseOne step outside the crossing, fewer beams overlap, so the dose drops within a few millimeters. The nerve beside the tumor sits on that slope.

Axial section through the head, schematic. Sixteen beams are drawn; the Gamma Knife uses up to 192. The address is an example in Leksell coordinates.

Another way

Move one beam instead of fixing many. A linear accelerator sweeps its beam in arcs around the tumor, and the CyberKnife carries one beam on a robotic arm to many positions.

BecauseBoth keep the same geometry, many directions and one crossing. The directions are spread over time instead of over sources.

Check

If 192 beams each give 1/192 of the dose, they add to the whole dose where they all cross: 192 × 1/192 = 1. A point on one path alone receives 1/192, about half a percent. The arithmetic ignores scatter and attenuation.

KeepWeak on every path. Strong at the crossing.

The day job

Igor Barani treats only tumors of the brain and spine. His practice is neuro-oncology seen from radiation oncology, with the Gamma Knife, the CyberKnife and linear accelerators. At Barrow Neurological Institute in Phoenix he is Professor and Chairman of Radiation Oncology. His published work is listed on PubMed.

7h Correspondence

Letters

igor@barani.org

Patients and referring physicians should contact Barrow Neurological Institute directly. Medical questions cannot be answered through this address.

Published work is listed on PubMed.

Colophon

Set in Hanken Grotesk by Alfredo Marco Pradil, standing in for Barani Sans until its release, and in Doto, a dot-matrix typeface by Óliver Lalan. Star positions come from the Hipparcos-based catalog in d3-celestial by Olaf Frohn, for epoch J2000. The line on the opening page is computed in your browser from your device's clock: the local sidereal time in Phoenix, and the height of the first point of Aries above the horizon there, ignoring refraction. The pages run from 0h to 7h of right ascension, from the first point of Aries past the June solstice, and the chart follows the ecliptic as you turn them.