Author: Sandhiya

-SandhiyaBala

STEM Land was invited to Salem to conduct a three-day capacity-building and Electronics workshop with the Students of 7^th and 9^th grade along with all the teachers at Vidhya Peetham School. The workshop aimed to engage with the Students and Teachers and help them understand basic Electronics and on building leadership skills in the teachers and students using Radical Transformational Leadership Tools (RTL) (Monica Sharma, 2017).

Day-1(On 23rd August 2024)

Morning Session:

We introduced ourselves using our universal values which made the students and teachers curious about the same. The introduction was followed by a session Stand & Fear Tool where the students and teachers identified and enquired about their universal values and how they can harness them to face their fears. After this we gave a brief introduction on Mathegramming and our core values, we proceeded the workshop with the foundational concepts of electricity, creating a truly dynamic learning experience!

Purpose: Empowering Minds and Energizing Learning

The primary goal of this workshop was twofold:

•  To help participants tap into their inner strengths and develop leadership skills.
• To provide a solid understanding of Electric current and its principles. This included learning about charge, voltage, current, power, and energy.

Later, Dinesh introduced the exciting world of electric currents, explaining fundamental concepts and giving exercises to solidify understanding. Participants learned about household electricity, types of batteries, and even calculated energy consumption!

Afternoon Session:

Post-lunch, the mood was lightened with a fun video and a dance session (Thought break), and we introduced Deep Listening and Background Conversations with both Students and Teachers. The session incorporated time for reflection they can reflect on the past and apply what they learned to think about what they could have done differently.

Using materials like LEDs, multimeters, and connecting wires, students explored real-life applications of electrical concepts. They tested conductivity, and body resistance, and learned the differences between poor and good conductors. The hands-on activities not only deepened their understanding but also made learning incredibly fun!

Outcomes:

Day 1 of the basics of electronics workshop was a remarkable success. Participants discovered their inner values, learned to face their fears, and Deep Listening and Background Conversations, and gained a thorough understanding of electric currents. They didn’t just learn the theory—they lived it!

Electronics and Circuits Workshop – Day 2(On 24rd August 2024)

The second day started with a two-minute stillness and focused attention on breathing, then we introduced to the four profiles i.e., an RTL Tool to understand different parts of our identities.

The purpose of Day 2 was threefold:

• To guide participants in connecting with 4 profiles and types of Complaints tools.
• To deepen their understanding of electric circuits, resistors, and the practical application of these concepts.
• To start to give the exposure of kirigami to children.

Morning Session:

Saranya kicked off the session with exercises that encouraged students to connect with their inner values and introduced 4 profiles. This was followed by a discussion where each group shared their insights on stage. Dinesh kickstarted the electronics and circuits workshop taking the stage to explain the essential concepts of electric circuits and the function of resistors. Students learned to calculate voltage and current using resistors and LEDs, exploring these concepts hands-on with multimeters, and breadboards. The activity was not just about theory; it was about seeing, touching, and feeling the flow of electricity!

Afternoon Session:

The afternoon kicked off with an energizing video and dance(thought break), recharging everyone for more learning. we reconnected with RTL tools and explained the three types of complaints. This made them see complaints from a different perspective rather than usual.

Participants learned to work with seven-segment displays, understanding how to use switches to control the flow of electricity. The fun didn’t stop there! A creative craft session led by Sowndharya introduced the art of kirigami. Students crafted intricate paper balls, enhancing their concentration and creativity. This unique blend of electronics and art not only made the learning experience holistic but also incredibly enjoyable!

Outcomes:

By the end of Day 2 of the electronics and circuit workshop, students gained invaluable insights into their inner strengths and the practical application of electronic concepts like resistors and seven-segment displays. The creativity and teamwork on display were truly electrifying! 

Day-3

On the last day(Sunday), At First, we planned to take the advanced electronics session only for teachers but the effectiveness of the last two days’ workshop triggered students to participate even on Sunday to take part in the session along with teachers.

We hadn’t expected students to show so much interest and join the optional session on Sunday.

They learned types of switches, connecting 2 letters/ numbers (7-segment display) in the breadboard, and potentiometer to vary the resistance.

In the afternoon we introduced scratch and polypod to explore mathematics visually. In Polypod children were also to project on their own with the guidance of the mentors.

Samvatsar in contrast to Samvat

            Samvatsar which earlier meant a year, now does not represent the year any longer. Instead, it represents the time it takes Guru (Jupiter) to move across one rashi. The Jupiter cycle is nearly 12 years. Hence, we get kumbha mela every 12 years which follows this cycle.

            The cycle of 60 years (also followed by the Chinese) comes from the fact that a cycle of Saturn takes 30 years and the LCM of 12 (Jupiter’s cycle) and 30 (Saturn’s cycle) is 60. At the end of a 60 year cycle both Jupiter and Saturn will be back to the original position. These years also have names:

1) Prabhava … to 60) Akshara, but the Chinese have given them names of animals which are more popular.

Celestial equator, Latitude, longitude and celestial coordinates systems

            As we have seen, the earth is a sphere which rotates around an axis, the two points at which this axis passes through the earth are called the poles (the north and south pole)

The equator is a great circle on the earth equidistant from the two poles. The equator divides the earth into two parts called the north and south hemisphere.

To decide the latitude and longitude of the given point P. We use a secondary circle which passes through the two poles and point P. Let the circle intersect the equator at Q. The arc PQ measured in degrees is called the latitude of P.

To measure the longitude, we need another circle passing through the poles called the prime meridian. In India the prime meridian was taken to the secondary circle passing through Ujjain.

Nowadays it is taken to be the circle passing through Greenwich. Let the prime meridian intersect the equator at O. The arc OQ is called the longitude of P.

Celestial coordinates          

            This system of coordinates on earth is extended in various ways to the celestial sphere. We imagine that all the stars and planets in the sky are on a very large sphere called the celestial sphere.

The poles are extended to intersect the space as the celestial North and South poles. Consider the plane containing the earth equator. If we imagine that it is extended indefinitely, this plane will intersect the celestial sphere in a circle called the celestial equator.

The Celestial prime meridian is called the first point of Aries or the vernal equinox. It is denoted by y , the greek letter gamma, because that symbol resembles two horns of a ram, and is the zodiac symbol for Aries. Even though this has moved it is still called the first point of Aries.

So a circle through the poles and y also intersects the celestial equator at
y . And the angle y Q is called the right ascension abbreviated to RA (corresponding to the longitude) and the rotation up is called declination abbreviated by dec (corresponding to the lattitude).

            A daily table of star and planet position is called an ephemeris. Software C2A can generate the ephemeris table. There are also python packages like pyeph and skyq that can give accurate information on the same.

Ecliptic coordinates

            In a second system of coordinates, one uses the ecliptic circle or plane instead of the equatorial plane. The ecliptic plane is around 23’ off from the equatorial place and the vernal equinox (and its diametrically opposite point on the celestial equator) is there the two meet.

The ecliptic plane is the plane in which the earth orbits around the sun or equivalently, the plane in which the sun is observed to move in the sky.

            A line from the center of the ecliptic circle, and perpendicular to its plane, intersects the celestial sphere in two points, again called ecliptic poles.

           We use a great secondary circle from the ecliptic poles through the point P and let it intersect the ecliptic circle at Q. The angle PQ is called the celestial latitude. The celestial latitude of the ecliptic plane is zero.  The prime meridian remains a great circle through the ecliptic poles and the first point of Aries ???? which point is at the intersection of the ecliptic and equatorial planes. The angle ???? Q is called the celestial longitude.

For this purpose, there is a third coordinate system called the ALT-Azimuth system. In this system, the basic plane is the one which passes through the position of the observer on earth and the horizon.

Precession of the equinoxes

            This precession of a rotating object is observable in an ordinary top. While the top spins about its axis, the axis itself rotates. This rotational motion of the axis is called precession.

            The same thing happens in the case of the earth. Not only does the earth rotate about its axis, the axis itself slowly rotates pointing to different parts of the sky and different times.

            Thus, the axis currently points to what is called the pole star. But this star was not the pole star 1500 years ago and will not be 1500 years later.

            The precession is rather small 50.3 arc seconds per year (an arc second is 1/60 of a minutes which is 1/60 of a degree) or precession is about 1° in 71.6 years or 360° in 25,772 (or 26000 years the rate of precession may vary a bit)

What the difference does that make?

            This extra rotation of the axis of rotation itself adds a small amount to the rotation speed of the earth around the sun.

How much?

            The sun revolves around the sky 360° in one sidereal year, of 365.26 days. So, it covers 1° in 365.26/360 days. Therefore, it covers 50.3 arc seconds = 50.3/3600 degrees in 50.3/3600 x 365.26/360 days.

            Since 1 day is 1440 minutes, this amounts to 50.3/3600 x 365.26/360 x 1440 = 20.4 minutes. That is because of precession, the time from equinox to equinox = the tropical year is less by 20.4 minutes than the sidereal year or the time it takes for the earth to revolve around the sun.

First point of Aries

            As a result of precession not only does the pole star change with time but so do the equinoxes and the constellations. The north celestial pole, decided by the earth’s rotation axis, is always perpendicular to the celestial/earth equator.

            So when the axis rotates so does the equatorial plane. The equinox is the point when the sun crosses the celestial equator.

            That is, it is at the intersection of both ecliptic and equatorial planes. This intersecting point will change with the movement of the equatorial plane.

            That is the vernal equinox or the first point of Aries will change with time. In fact, the vernal equinox is no longer in the Aries constellation. It is currently in the Pisces constellation.

Now what coordinates does one use to measure this movement?

            A difference of 0.5° in 35 years may not seem like a lot but especially for space science it can be a huge difference because distances in space are huge.

            Therefore, NASA offers a choice of various coordinate systems, J2000 refers to the equinox of the epoch of 2000 CE or one can use the current equinox, called equinox of date etc.

What to do in the context of Indian astronomy and the Indian calendar?

• The first approach is that the “first point of Aries” means what we actually observe as the first point of Aries (mesh). This is called the Nirayana or Sidereal system. Therefore, there is a difference between sidereal and tropical longitudes, the difference is called ayanamsh.
• Western ephemerides usually follow the tropical system with the idea that star positions given in star charts are to be updated every 50 years. The Indian approach has both systems.

Panchang

            The panchang has 5 elements, we already learnt three tithi, vara and nakshatra. The other two elements are karan and yoga which we will not be using.

            The scientific panchang has only the 5 elements of samvat, maada, tithi, vara and samvatsar.

            A karan is just half a tithi so there are 60 karana’s. These are divided into 4 fixed karan plus 7 moving karan to reduce to 11. The 7 moving karan’s repeat 8 times in a chandramas of 30 tithi’s = 60 karan’s. The 4 fixed karans are kimstughna, sakuni, catuspada, nagava. The 7 repeating karanas are Bava, Baklava, Kaulava, Taitila, Garaja, Vanija, visti.

How to calculate karana

            This is a simple process of dividing the difference in longitude of moon and sun by 360’ (minutes corresponding to the 6° as it is half of a tithi which is 12°) and then adding one in the shukla paksha and diminishing 1 in the krishna paksha.

Yoga

            Yoga (pronounced Yog)here means sum (not yoga which means union of atman and brahman, but misunderstood as hatha-yoga = physical exercises). The yoga in astronomy/astrology is the sum of the celestial longitudes of the sum and the moon. Modulo 360° and divided by 13°20’ to get a number from 1 to 27 as in the case of Nakshatra’s.

            That is. It is the time in which the sum of the longitudes of the sun and moon modulo 360 increase by 13°20’.

Yoga mentioned in the Panchang is not found in Surya Siddhanta. Aryabhatiya or Laghu Bhaskariya etc. Its scientific significance is not clear.

The Drk Panchang (Lahiri)

            There are two ways to correct the texts of Indian astronomy one is to attempt to calculate all that has changed. The other is to use the understanding and relate it to the current observations (e.g. of the pole starts, etc)

             The word Drk comes from Drshti i.e. relates to current observation. This panchang is based on the ephemeris (position of sun, moon etc) actually observed. The starting point is the ephemeris published by NASA Jet Propulsion Lab (JPL).

            That is a tropical (sayan) ephemeris which must be converted to a nirayana using one of the various systems of ayanamsh.

            This JPL ephemeris had been packaged for astrology by the “Swiss ephemeris”. The original release of the software in 1997 was based on the DE405/406 ephemeris. Since release 2.00 in February 2014, it is based on the DE431 ephemeris released by JPL in September 2013.

            The authors of the package Swiss Ephemeris are Dieter Koch and Alois Treindl sold by the company Astrodientist AG, Switzerland.

            It also has a table of the Lahiri Ayanamsa used in the Indian national panchang one of whose authors was N. C. Lahiri a mathematician, and part of the Indian calendar reform committee set up after Independence.

To calculate the Ayanamsa it is necessary to set the starting date and time. Lahiri ayanamsha = 23° 15 ’00’’.658 on 21 March 1956, 0:00 TDT (Terrestrial dynamical time). Reference star Spica, its J2000 longitude is 170° 58 ’58’’. Then calculate precession for any time from that value and the given model of precession.

To calculate the panchang for a given Gregorian date. The procedure is to take a Gregorian date and convert it to Julian day which is easily related to Ahargana as explained above. Ahargana = jd – 5888465.5.

For that Ahargana we can immediately calculate the Kali samvat or the number of Kali years elapsed using the duration of the sidereal year,

     Kali samvat = integer part of (ahargana / duration of sidereal year)

Now we have precise position/longitudes of sun and moon from the ephemeris for the Julian date. We then convert it to tithi.

Traditional method of calculating tithi

            Traditional Indian astronomy texts give the revolution numbers for the various planets. Example as stated in the Laghu Bhaskariya 9-14

Calculate the Ahargana as explained in Laghu Bhaskariya

Different authors have different values (Table from Rao)

These mean (average) motions are obtained as follows,

            Example 1: As per table on Aryabhata, if in 4320000 (sidereal) year there are 1577917500 civil days, then in 1 (sidereal) year there are 157791 7500 ÷ 4320000 = 365.258680 days compared to the modern value 365.25636 days.

            Example 2: If the moon makes 57753337 revolutions in 157791750 civil days, then it makes 1 revolution in 1577917500 ÷ 57753337 = 27.321668 days = sidereal month, modern value 27.321661 days.

            We can easily get the mean motion of the moon. If in 27.321668 days the moon moves 360°, then in 1 day it moves 360/27.321668 = 13.176355°, very slightly different from its modern value 360/27.321661 = 13.176358°. Hence, in 1 day the moon approximately covers 1 Nakshatra = 13.33°.

            Likewise if in 365.258680 days the sun covers 360° then in 1 day it covers 360/365.258680 = 0.9856°. Hence, it covers 1 rashi = 30° in 30/0.9856 = 30.438 days.

            In these revolution numbers, given in all traditional astronomy texts, the revolutions of the sighrocca of the inferior planets Mercury and Venus are given. This corresponds to their revolutions about the sun.

            Since the sighrocca as seen from earth occurs at “superior conjunction” when their relative velocities of rotation around the sun are most different.

The mean motion obtained above enables the calculation of mean longitude of sun and moon and planets for a given ahargana. These are mean values and the planets do not move with uniform speed as the very existence of mandocca etc. shows.

Obtaining the truth or values required a series of corrections called the manda and sighra corrections. These use the epicycle model to explain who the planets are slowed down or speeded up.

            In this epicycle theory, the mean planet moves with its mean velocity in a circle round the earth (from west to east), the true planet moves in a smaller circle with its center on the mean planet, in the opposite direction from east to west. The faster and slower motions are then explained by adding the two velocities.

Indians had a clear idea of the cause of eclipses

            Aryabhata stated this explicitly

However, many historians insist that Indians were superstitious and thought that eclipses are due to demons rahu and ketu.

            In fact, Lalla in his 20th chapter denies the demonic theory of eclipses very explicitly. Stating if they were indeed demons then why is it that we can predict accurately when these are going to happen.

Solar eclipses

            A solar eclipse is caused by the moon coming between the earth and the sun, obstructing our view of the sun so that the shadow of the moon falls on some point of the earth.

When does an eclipse occur?

            This can happen only when the sun, moon and earth are very nearly in a straight line. This does not happen at every full moon (purnima, lunar eclipse) or new moon (amavasya, solar eclipse)

Moon’s orbit and ecliptic

            Because, the plane of the lunar orbit around the earth is at an angle to the plane in which the sun appears to revolve around the earth. The angle is about 5° 7’ 47.9’’.

Why a solar eclipse does not happen every amavasya?

            A solar eclipse does not happen at every amavasya, but can take place only when both sun and moon are near one of the moon’s nodes called Rahu and Ketu; these are the two points at which the orbit of the moon intersects the ecliptic.

Conclusion:

In this session, we explored the ideas of C. K. Raju, who showed us that it’s okay to think differently and question old ideas. His work in mathematics, especially with time and calculus, teaches us that learning is not just about accepting what’s already known, but about exploring new possibilities. As we finish, let’s take inspiration from C. K. Raju and always be curious, willing to learn, and open to new ways of understanding the world around us.

Synodic month

            The month that is used to determine festivals etc (including most Indian festivals) is called the synodic month or the month of phases of the moon. A synod is a gathering of priests or religious groups where the important day would be declared by e.g. sighting of the moon. However, this is a misnomer in India as Indians knew how to calculate the phases of the moon. First thing to understand is that the sun shines by its own light, whereas the moon and planets shine by reflected light. And half of the moon and each planet (except sun) is always dark.

Therefore, it is a new moon (or perhaps no moon) when the sun and moon are exactly on the same side of the earth and from earth we only see the side of the moon in shadow.

The full moon, when the sun and moon are on the opposite side of the earth and we see the bright side of the moon.

Some of the children asked how we are able to see the moon when earth is in between and he explained that there is a difference in the planes of the revolution of the moon around the earth and the earth around the moon (around 5’) and occasionally the two planes meet which causes eclipses.

Tithi

            Tithi is simple and elegant system which Indians worked out to moon’s phases. A tithi is the time in which the moon moves ahead of the sun by 12°. More precisely, it is the time in which the celestial longitude of the moon increases by 12° over the longitude of the sun.

[Inter day the moon moves around 13° and sun around 1° in one day, so the relative movement of 12° as a measure of ‘day’ is sensible.]

A full rotation of 360° with a relative speed of 12° would give us 30 titis for the sun and the moon come back the same relative position separated by 0° or 360°. That is, 30 tithi’s is the time from full moon(purnima) to full moon or from new moon to new moon. This period of 30 tithi’s (not days) is called a synodic month. Tithis is not a day!

The tithi’s are divided into two groups of 15 tithi’s:

• शुक्ल पक्ष (shukl paksh), waxing phase of the moon.
• कृष्ण पक्ष (krshn paksh), waning phase of the moon.

[To remember this we can think of Krishna – dark sot he krish paksh makes the moon from bright to dark.]

            In each phase, the tithi’s are counted in sanskrit number 1 to 14 and then the amavasya or purnima for the 15th tithi. This simple scientific system can be used because there are always 30  tithi’s in a month.

            Names of tithi’s,

In terms of days, a synodic month is 29.53 days. Why is the synodic longer than the sidereal month of 27.3 days?

In 27.3 days or 1 sidereal month, the moon has orbited the earth once. But in this time the sun has moved by about 27° relative to earth (or the earth has moved by about 27° round the sun). So the moon must move by another 27° round the earth. Since the moon moves by about 13.33° a day round the earth, this would take it a little over 2 days, plus a fraction for the 2° earth/sun movement in the extra 2 days in between. That is why the synodic month is about 2.2 days longer than the sidereal month.

How to calculate tithi?

Why 720 minutes? As 12° = 12×60’ = 720’

Two Complications

            There are complications in this scheme of things. The first is to link the “synodic” month of phases of the moon to the year or solar cycle. Not doing this would make a purely lunar calendar which will slip with respect to the solar calendar. The second is to link the relative motion of the moon and sun to the civil day which is based solely on the rotational motion of the sun.

The story of the colonized mind is that the Indian calendar is a lunar calendar. The Indian calendar is a luni-solar calendar.

            There is a simple rule for syncing the lunar cycle with the solar cycle. Whenever there would be no sankranti in a chandramasa, an extra chandramasa is added. This is called adhik (more) masa. This keeps the solar and lunar month in sync. This happens once within 3 years.

            In the rare cases when there is more than one sankranti in a chandramasa, it is treated as a kshaya (reduce) masa and dropped. However, in this case in that year there will always be a different adhik masa, so the number of lunar/solar months/sankrantu is at least 12. For example, if the sun transits into both mesa and vrsabha rashi in a chandramas, then it will be called chaitra-vaisakha ksaya-masa. There will be no separate months labeled chaitra and vaisakha.

            Likewise to keep tithi synchronized to civil days, there can be added or removed tithi. Thus, a true tithi is always the time for the moon to get ahead of the sun by 12°. However, to decide when to celebrate festivals and map it to a ‘civil tithi’, the tithi prevailing at sunrise is assigned to the civil day.

            A tithi or the time in which the moon gets ahead of the sun by 12°, can be longer or shorter than a civil day. It is possible for a tithi to continue across two civil days as well.

Seasons

            An important function of the calendar is to tell the seasons, this was very important for India which was for thousands of years and agricultural society.

            For example, when is the right time to sow? When is the right time to reap?

           In the west there are only two seasons, hot and cold, though the intermediate periods go from summer to winter and from winter to summer. However, rains can occur throughout the year.   However, on the Indian calendar every two months there is a different season so there are six seasons.

Vedic names for months

            The earliest vedic names for months are from before the vedanga jyotisha. They named month according to season, not nakshatra or lunar phase.

Many of us think that the summer and winter are due to the distance of the sun from earth. Actually, the hot and cold seasons are because the axis of rotation of the earth is tilted to the ecliptic or the plane of the observed orbit of the sun (suryavrtta).

When the Northern hemisphere faces the sun it is summer in the north and winter in the south. When it faces away it is winter in the north and summer in the south.

Geocentric vs Tychonic vs Heliocentric vs Barycentric

He explained the various models of the solar system that were thought of and followed to model what was seen in the sky.

Geocentric model

Geo(earth)centric model is what you actually observe, the sun, moon, planets, going round the earth in the sky.

Tychonic model

All other planets go around the sun and the sun with all the planets goes round the earth.

Barycentric model

            Moon and earth or sun and earth rotate about a common center of mass because earth is massive compared to the moon, and sun is massive compared to planets. This barycentric often (but not always) lies inside the more massive body.

Rainy season

            A season unique in the calendar and not found in the western calendar is the rainy season. It’s not found in the western calendar since there is no specific rainy season in Europe. But in India the major season is the rainy season because the entire economy and reproductive cycles of animals depend on it across India.

            Whereas the heat balance decides hot and cold seasons, the rainy season is decided by the moisture balance and the wind regime. There is no direct one-one relationship between solar motion and rain.

            Going by the western calendar often leads to the phenomenon of delayed monsoons. He believes there is a causal relationship between the motion of the moon and the wind regime for monsoons. He showed a few newspaper images as an example of delayed monsoons.

Rainy season and culture

            Rainy season is when all life on the subcontinent reproduces. Easy availability of food.

            He showed a few bollywood songs to children about how the rainy season played an important role.

Festivals

There are broadly two calendar systems

• The amanta ends with amavasya, beginning with sukla paksa pratipad.
• Purnimant ending with purnima, beginning with krishna paksha pratipada.

            The festival which falls in the shukla paksha belongs to the same month in both calendars. A festival which falls in the krishna paksha will be a month earlier in the amanta system.

            Example: Diwali is on amavasya in the krishna paksh. As per amanta calendar, five days of Diwali festivity span over two months.

• Diwali begins – Krishna Paksha Trayodashi(28th tithi) of Ashwin(7th month)
• Diwali ends – Shukla Paksha Dwitiya(2nd tithi) of Kartik (8th month)

            As per Purnimanta Calendar

• Diwali begins – Krishna Paksha Trayodashi (13th tithi) of Kartik(8th month)
• Diwali ends – Shukla Paksha Dwitiya(17th tithi) of kartik(8th month)

            The civil days are the same in both cases, but the names of the months are different. Festival based on the Sankaranti is Makar Sankranti or Pongal transit of sun 15 jan 2024

            Festivals based on christian calendar are Republic day 26 Jan 2024 and Independence day 15 Aug. He asked children whether it is good or bad to have the most important Indian festival based on the christian calendar.

Weekdays

            Apart from the vast majority of stars, which move in an orderly fashion, there are seven celestial bodies which move in a more erratic fashion. These bodies are called planets. In ancient usage, the seven planets or wanderers in the sky, including sun and moon. The vara or 7 days of the week, are named after the planets.

            The 7-day week is common across several cultures. Sunday, Monday and Saturday are clearly named after the sun, moon, and saturn(shani).

Tuesday is derived from “Tiv’s day” which is named after the Norse god of single combat. Among the norse gods and goddesses, Tyr is identified with Mars. Tyr[Mars = Mangal, and Managalvara].

Wednesday is derived from “Wooden’s day”. Wooden is identified with Mercury [Mercury = budh and budhvara].

 Thursday from “Thor’s day”. Thor is identified with Jupiter [Jupiter = Guru and Guruvara].

Friday from “Freya’s day”. Freya is identified with Venus [venus = shukra and shukravara].

He asked is there any reason for the order of the weekdays? Which is original? If it is an Indian one. Why?

The logical explanation for this order of the week day is available only in the Indian tradition. This explanation relates to the seven planets that wanderers visible to the naked eye are as follows.

Aryabhata orders the planets according to the observed speed of movement.

The day is named after the lord of the day = the lord of the hour prevailing at sunrise. “The fourth in order of speed are the lords of the successive days reckoned from sunrise(at lanka)”

The chart for the lords of the first hour of each day. That tells us why the weekdays are in the given order.

Time and angle measurement

            Most of us must have heard of popular terms like muhurta. He asked what does the term muhurta mean?

            Vedic timekeeping (before the use of hours) was successively sexagesimal. Instead of 24 hours of 60 mins in a day, a day had 60 ghatis (of 24 mins), each ghati had 60 pala (of 24 seconds), each pala has 60 vipala (of 0.4 seconds).

            Two Ghatis is a muhurta.

Converting hours, min, sec to ghati, pala, vipal

            E.g. Convert 10 h 30 m 12 s to ghati, pala, and vipala.

Divisions of time

            There were finer divisions of time such as (1/33750) which were not used in everyday life called murta.

            1 prana = time for 1 breath = 4 sec (15 breaths per min)

            A common unit was the yama (pahar) consisting of ⅛ of a day and night or 3 hours measured from sunrise. Thus, do pahar = six hours from sunrise = noon.

Yuga System

            There were also very large measures of time in the yuga system found in the Surya siddhanta and in the vishnu purana etc.

These large measures of time puzzled the early British colonizers who had never encountered such large numbers before.

            One reason for these large numbers is clear. They represent higher precision, which needs precise fractions.

            There is also a difference between Aryabhata and Surya Siddhanta. Aryabhata has all four yuga’s of equal duration.

Year and 60 year Jupiter cycle (samvat and samvatsar)

            There are 3 popular systems of naming years, Kali samvat, year count starts at -3101 CE (=3102 BC), Shaka samvat +78 CE and Vikram samvat its start date is -57 CE.

            In the Hindu version of the preamble of the constitution of India, the date of its adoption (26 November 1949) is presented in Vikram samvat as Mrgsheersh shukla saptami samvat 2006. In this case 57 years are added in November.

Complication 1

            The Indian calendar uses sidereal years not the tropical years used by the Gregorian calendar. Thus the number of years to add or subtract from the Gregorian calendar will depend on the month.

Complication 2

            A calendar has to be recalibrated for the place since the times of sunrise varies from place to place and the civil day and civil tithi are decided by the time of sunrise.

The change in time of sunrise depended on the longitude was known as shown above. yavakoti must be east of Lanka by 6 hours, Siddhapura must be east of yavakoti by 6 hours and Romaka must be west of Lanka by 6 hours (or east of siddhapura by 6 hours).

Note that like Lanka, these are not actual places, but four points on the equator 90° apart.  All four points are in the midst of the Ocean.

Because of variations of time and sunrise with longitude, the panachang calculations are done for the prime meridian (yamyottari) passing through Ujjain and Lanka.

            The word Yaama, as already explained, is a vedic term for a period of 3 hours. The time difference is 1 hour per 15 degrees of longitude per 360 degrees in 24 hours i.e, it has latitude 0 and the same longitude as Ujjain which was earlier treated as longitude 0 degree. Later this system was copied by the British who made the meridian through Greenwich as longitude 0 degree and also GMT clock time 0.

Summary of Previous session.F

• An angle is not about two straight lines meeting at a common point.
• Latitude and longitude are angles on the surface of the earth which cannot be measured using that definition or a protractor placed at the center of the earth.
• Angle is the relative length of the arc. Hence a protractor is shaped like a semi-circle.
• Angle(arc) measured relative to the circumference in degrees.
• Angle(arc) measured relative to the radius in radians.
• Indian prime meridian is meridian through Uijaini, Rohtak, Kurukshetra, Lanka (!= Sri Lanka, Its a point on the equator)
• Both angles and time are measured using the Sexgesimal system and can be used interchangeably.
• With respect to a time in the day the sun moves from west to east approximately 1° each day and the moon moves from west to east approximately 13.3° each day.
• The Indian system of time measured is Fully Sexgesimal.

   1 day = 60 (ghati = nadi of 24 mins), 1 ghati = 60 pala (a pala 24 seconds), 1 pala = 60 vipala(= 0.4s)

Homework: What is the proof of Thomas Macauly’s “immeasurable superiority” of the west?

(Sorry, no weapons of mass destruction found)

Proof 1 – Crosus conveyed to King Solon that the year was 375 days long

Proof 2 – Roman calendar needed to be corrected and for correction 448 days needed to added that year

Proof 3 – Cesar conquered Egypt and asked them to help correct the calendar.

Proof 4 –

• Egyptians had a fraction (“Eye of Horus” fraction) but Romans didn’t. The Romans could only accept 365 ¼ days which was wrong. Even for this the Egyptians then had 7 months of 30 days alternating with 5 months of 31 days (210+155 = 365 days) plus a leap year system adding an extra day every 4th year.

Proof 5 – Inspite of being given instructions the Roman took 20 years after the Julian calendar reform to understand that system and in these 20 years they did a leap year every 3 years. They counted the first year as year 1 and did the leap year when they reached 4.

One day was removed from February and given to August (Augustus) for this feat.

Proof 6 –

• Roman calendar was adopted as the official christian calendar in the 4th c.(1st council of Nicea)
• Changes to the year-of-the-lord(AD-BC) calendar in the 6th c.
• As a result the date of the equinox slipped by 10 days by the 15th c.

Proof 7 –

• It is necessary to correct it for navigation.
• By this time, the west has learnt a fraction from India via Fibonacci.
• And Introduced in the Jesuit curriculum by Calvius ca in 1572.
• Gregorian calendar reform still use leap year(hence equinox still does not come on fixed day)
  • Leap year every 4 years
  • But, not every 100 years
  • But, every 1000 years
  • Phew! Now the equinox will be correct on an average every 1000 years, but incorrect every year.

What about the smartness of colonized Indians?

• On Maculay’s advice and colonial education we learn to trust the west and distrust anything from India
• We trust Wikipedia
• We trust those who came here for wealth and reduced Indian from one of the richest countries in the world to one of the poorest
• We trust those who killed 50 million Indians through their systematic policies e.g. during the Bengal Famine.

Sidereal day and year.

            Indian tradition used sidereal days and the sidereal year. The sidereal day is the time for the earth to make one full rotation about its axis (with reference to a distant star). The sidereal year is the period in which the earth makes one revolution around the sun (with reference to a distant star).

Why is a sidereal day shorter by about 4 minutes than the tropical or civil day?

            First, the earth rotates in the same direction as it revolves around the sun. After one full rotation that star is seen again in the same place, say directly overhead. This creates a parallax error due to the closeness of the sun and the star being much further.

Parallax

            When you move, a distant object seems to move with you, nearby objects seem to move past you. As you drive the trees will look like they are going to pass you, but the moon looks like it is moving with you.

            He gave an example with the experiment to perform with two pens, one at 1 meter and other at 5 meters distance from the eye. Children did the experiment and found there is a relative motion between two objects.

            The sun is nearby compared to the star. In time the earth rotated once about its axis. It has also moved around the sun. So, the sun is seen in a different position due to parallax. A little more rotation is needed to bring a point on the earth back to the same position directly nearest to the sun.

How much extra rotation?

The earth is moving around the Sun in approximately 360 days i.e. approximately 1°. When the sun is seen from the earth at the same time every day it will look like it is moving 1° from west to east. As the star is far and does not move as seen from earth in one day the sun moves by approx 1° relative to the star as seen from earth. From earth’s perspective, it also takes 24 hours for the sun to rotate 360 degrees round the earth or 15 degrees in 1 hour. So, it takes approximately 4 min for the earth to rotate to its axis that extra 1°.

That is the approximate difference between the sidereal day and the tropical or civil day.

Venus spins in the other direction as it rotates around the Sun so the Sidereal day there is longer than the tropical day.

Inter day vs Intra day

We watched a demo in which we picked a time of day and moved the dates to see how the moon moves every day at the same time. This helps understand the Inter day vs Intra day movement.

A constellation is a group of stars near the ecliptic (observed path of the Sun). For our scientific purposes these are 30’ apart. In India we had Nakshatras initially; these constellations of Rashi’s came later. There are 12 of these corresponding to the ‘Sun signs’ and are used to see the movement of the Sun (during sunrise).

These are Masha – Aries, Vishuv Taurus, etc. Sankranti (every month) is when the Sun enters a new constellation. The Indian calendar follows a luni-solar system.

Summary

Rashi’s mark a region of 30’ in the sky

Sum moves approximately 1’ in each day

Sun takes on an average 30 days to move from one to the other

Sankranti is when the Sun enters a new Rashi

Nakshatra – are used to measure the movement of the Moon (west to east 13.17’)

Hence they divide the sky in 27 regions in the sky which are 13.33’ apart close to the time it takes the moon to go around the Earth. Covers 1 Nakshatra in 1 day and is considered the sidereal month (actually 27.321582’) hence spends more time in one Nakshatra (Rohini)

Horoscope

Not that you should believe in one, but understand what it has. Has the other circle corresponding to the Nakshatra and Inner circle corresponding to the Rashis.

The Laghu Bhaskara evaluates the angle of the Nakshatras by dividing by 800 minutes. Why 800 minutes? 13’20’ = 13*60’+20’  = 800’

-Preethi and Sanjeev

C.K.Raju started the session with a short summary of yesterday’s session.

Models of Christian Chauvinist History:

He explained that many people wrongly mix up Indian astronomy with astrology, which is often seen as a pseudoscience.  He highlighted that India had a scientific theory that the Earth is a spherical body that floats freely in space without any physical support. This was important for a good calendar and needed for understanding the concept of day and other observed phenomena. He pointed out that this concept was known in India long before it became widely accepted among Europeans. That Indians opposed the false claim in religious texts that the earth was supported by a tortoise or Sheshnag, etc.

In contrast with the Europeans who did not challenge the Bible that the earth was flat. He explained the Greek belief that the Atlas holds up the Earth. He uses this as an example of how ancient Greek ideas were more superstitious than scientific.

He mentioned  that Indians were using trigonometry as early as the 5th century. The accuracy of these trigonometric values were needed for accurate calculation of the Earth’s radius as well as for navigation.

The European scholars took precise trigonometric values from Indian sources, but were unable to use them effectively and did not give proper credit to where they received this information.

Position and Motion on a Sphere

            As we are talking about a spherical object we need to learn about the position and motion on a sphere. Motion refers to the change in position of an object over time. Position refers to where the small object (“ a point”) is on the sphere. Since space is also spherical we would also need this for the position of a star, sun, moon, etc.

            He explained that both Latitude and Longitude are angles that are measured in degrees on the sphere.

What is angle?          

He enquired on what is the definition of an angle. An angle is defined in NCERT Class 6 as two rays which originate from a common point. He asked questions like why an angle is denoted by putting an arc between two straight lines? Why are we using a protractor to measure an angle? Why is the protractor a semi-circle? If you had protractors of different sizes then will they measure the same angle?

We are only taught to measure angles only on paper. Then how would we measure these angles of latitude and longitude made by imaged straight lines at the center of the earth? We would need to make holes in earth and measure the angle it made at the Earth’s core?

He gave the definition of the angle in the Hindi text book and pointed out that it was quite complicated, because this is not how angle was measured in India and the language lacked the terms needed. Instead he stated that angle is defined as a ratio of arc length to either the circumference (degrees) or to the radius. When an angle is measured relative to the radius of the circle, it is measured in radian. When the circumference is divided into 360 pieces (or more) then the length can be measured by how many of these pieces are covered by the arc giving the angle in degrees. The circumference and radius of the circle are proportional i.e. they track with the size of the circle. Hence the measured angle does not depend on the size of the protractor.

This allowed for making measurements on the surface of the earth rather than dig inside :). This is still not an easy task as it involves long curved distances. Further, to convert these distances into an angle of the longitude and latitude, we need to know the circumference of the earth.

He explained that the earth rotates about an axis. The point which the axis passes through the earth is called North and South poles. A great circle is a circle whose center is the same as the center of a sphere. On earth, a circle through poles is a great circle. All longitudes are great circles. In the latitudes the only great circle is the equator. He explained to the children with an orange cut in the center to show the largest circle will be at the equator or center.

Sexagesimal system for times and angles

            We were taught that 1 day consists of 24 hours, 1 hour consists of 60 minutes, and 1 minute consists of 60 seconds. But the Indian system is full of sexagesimal, a day consists of 60 ghati(24 mins) , 1 ghati consists of 60 pala, 1 pala of 60 vipala, etc.

            Likewise, an angle consists of degree, 1 degree is 60 minutes, 1 minute is 60 seconds, 1 second is 60 thirds.

12°34’24’’13’’’ = 12 degrees, 34 minutes, 24 second, 13 thirds

When we measure in the stop watch it no longer uses a consistent sexagesimal system as the minutes and seconds are in sexagesimal, but after that it uses 100 divisions.

What is a day?

A simple definition of a day is a time from sunrise to sunrise. More precisely, this is a civil day. A simplest calendar would be to count civil days (Robinson Cruso calendar) from a given starting point (epoch).

In Indian tradition, the usual starting day or epoch is the start of kaliyuga. (This is the astronomy Kaliyuga, time when all planets were in conjunction i.e. the first point of aries that occurs rarely. The Maya calendar also begins almost at the same epoch. In the Gregorian calendar, kaliyuga, starts in 3102 BC = -3101 CE (The difference of one year is because the christian calendar does not have a zero or negative number). The Mayan calendar starts at 3112 BC. The difference of only 10 years in 3000 years.

How do we know the starting date?

The start of kaliyuga is -3101 CE. The difference of one year is because the christian calendar does not have a zero or negative number.

Ahargana and Julian days

            The notation of ahargana (day count) is a very ancient notion in India. E.g. It is found in the Surya Siddhanta. But in western thought the corresponding notion of julian days is very recent. It appeared in the west in 16th c. In the 16th century, Jesuit missionaries were based in kochi. We collected knowledge from Indian mathematics and astronomy texts with the help of local Syrian Christians. The translating and sending this knowledge back to Europe to prominent people such as christoph clavius, Tycho Brahe, Julius Scaliger.

            In the 16th century, Ahargana was taken to Europe and Christianized as the Julian day number. This was so named by Julius Scaliger in 1583 a contemporary of Clavius after his father’s name, Julius Caesar Scaliger.

Julian day number is a Christianized ahargana

            The only difference from Ahargana is the choice of the start day or epoch which was selected as 1 Jan 4713 BC. The day that the universe began as per Christian belief.

            The only difference between the Kali Ahargana number (KAN) and the Julian day number(JDN) is a constant due to different starting epochs,

            KAN = JDN – 588465.54The (tropical) year, summer and winter

Sun rarely rises from the exact east. Only in two days of the year it will rise exactly in the east. The sun moves north 23.44° then moves south 23.44° east. The end of the movement, the exact two instants when the sun just stops moving and reverses direction of movement are called solstices (end of movement).

            There are two solstices, in the northern hemisphere the summer solstice or longest day and the winter solstice or shortest day.

            Daylight duration varies with the latitude. Aryabhat had commented that Gods (assigned to the north pole) and Asuras (assigned to the south pole) see the sun after it rises for half a year. Divine day is one year of mortals. 1 Divine year is 360 years.

In summer, when the north pole is pointing towards the sun, the day in the northern hemisphere are longer and nights are shorter. In winter the situation is reversed, days are short and nights are long. In the southern hemisphere the situation is the opposite, because summer and winter are the opposite of those in the northern hemisphere.

Equinoxes

            At sunrise the position of the sun keeps moving from east to 23.44° north and  22.44° south throughout the year. The two instants exactly midway between the two solstices are called equinoxes. Nox means Night. Equinox indicates that the day and night are the same length (at the equator). The vernal equinox marks the beginning of warmer season in the northern hemisphere, while the autumn equinox marks the beginning of the cool season, in the northern hemisphere.

            The earth (while revolving around the sun) is also rotating around its axis, which axis points to the north celestial pole, a point in the sky near the pole star, currently polaris.

            Summer and winter in the southern hemisphere are the opposite of those in the northern hemisphere. Hot and cold seasons are not due to distance from the sun, but the tilt of the earth.

Timekeeping is essential for organizing our lives, whether for daily tasks or cultural events. The Indian calendar system, unlike the western calendar, is scientific and most of our cultural festivals and activities are aligned to this calendar. C. K. Raju, an Indian mathematician and physicist, has explored the deeper scientific aspects of this traditional Indian system.

A Secular Calendar for a Secular Education (Country):

He explained that the Western calendar i.e. the Gregorian calendar is based on Christian traditions. Pope Gregory attempted to fix the Julian calendar (Julius Caesar ordered a calendar consisting of twelve months based on a solar year in -43 C.E.) to align the date of Easter in the 6th century. At this time he fixed the ‘0’ of the calendar. The way we count years like A.D. (The year of my dominator/lord) and B.C. (Before my savior Christ) also comes from Christian beliefs and attempts to place a time on the birth of Christ. Because of this, he argues that calling this calendar “secular” is misleading since it has clear religious roots.

He mentioned that the story without evidence is called Indoctrination. He describes how certain scientific and cultural ideas are accepted without question, often due to their widespread acceptance or authority. This happens because education and cultural stories focus mostly on Western achievements and don’t give much attention to contributions from other cultures.

Just from our date of birth which we define in terms of number of years from A.D. these ideas are subtly placed in our subconscious.

He gave an example with proof that in 1582 there was an unsuccessful attempt to convert Akbar and when this failed then to teach his son Murad Mirza and the first statements were not direct, but indirect indoctrination.

Education in the west was handled by the Church and only in 1870 the law was passed in the west to have a secular education. This was 370 years after the first missionary school in Indian (Kerala).

Many believe in TINA (There Is No Alternative)to keep the status quo of not having a secular calendar, but there is an alternative the Indian calendar as it was scientific was used by not just Hindus, but also Bhuddhists, Jains, Arabs, Chinese.

Our current education system never  gave a child the knowledge of the Indian calendar or its basis so we do not know enough to compare the two calendars to understand which is better. But, we assume that the western calendar is better, because we are told so and we don’t take the effort to learn and check.

Why do we assume the stories we are told are true?

A lot of the stories are built systematically. When the crusaders were in war the history was against the Pegans, There was knowledge in arabic books that were usually burnt, but as it was felt that they were behind in Science and Mathematics a new ideas was created that the Greeks had come up with all this knowledge and it had disappeared for 1500 years and was only being recovered and reclaimed from the arabs. This resulted in them translating the texts and claiming it as their own. He gave an example of the Christian Doctrine of Discovery in the 15th century (papal bulls) that anything discovered by a christian is alone a discovery. This included land and was extended to knowledge as well.

Indian Calendar and Science

Politics tend to play a role now and in the past in Science and Mathematics and even in modern Indian UGC introduced courses on Vedic astrology. While it is true that Indian calendars were used by astrologers, we need to distinguish between Jyotish (time keeping) as different from Phalit Jyotish (use of time keeping for astrology). It is important to keep a distinction between what is and what is not science.

What is science? What is a scientific theory?

Some ways to check science is that it is empirically testable or refutable (i.e. by experiment). As most texts present that in India there was no science: He gave an example of payasi who used 30 different experimental methods to empirically refute the belief of the soul or atman.

There can be theories that work fine for some time and given some context, measurement or discovery could be provided wrong in the future e.g. Newtonian mechanics was found to have limitations.

In India in the Nyaya Sutra – 2 four ways are given for proof:

१-प्रत्यक्ष (you an see), २-उपमान (make an analogy), ३-अनुमान (you can infer), ४-शब्द (belief in an authority)

He also presented his sources of information for the Indian Calendar

These included the Vedantic Jyotish work of Bhramagupra, Aryabhata, Lala, Chandra (Leelavathi), etc.

Round Earth (भुगोल) and Round Sky(भगोल)

The basis of the Indian calendar is that the earth is a sphere and revolves around the sun with the moon that revolves around the earth.

He asked for different ways in which the children could infer that the earth was in fact not flat. He presented how Aryabhatta had talked about the Earth being like a kadamba flower and estimated the size of the earth using trigonometry.

As the children in the section were young it was difficult to proceed mathematically and he talked about how the angles could be estimated and trigonometry could be used to determine the height of a tree, mountain.

A similar measurement from the top of a mountain could be made of the dip and the horizon.

It is likely we will take up the definition and measurement of the angles in the next session.

He showed various measurements of the radius of earth including yojana and later Al-Biruni made the calculations after coming to India to study the techniques in arabic miles that could be mapped to miles very closely.

He presented various arguments that were presented by the mathematicians to understand that the earth was round e.g. the tall tree that disappears in the horizon as light travels in straight lines. That the earth was not held by a tortoise as what is the tortoise standing on, etc to conclude that it was indeed the earth and not the sun that was rotating.

How the Indian Calendar Works

The Western calendar that we use is based only on the Earth’s journey around the sun, which takes about 365 days. The Indian calendar is more than just a way to track days and months. It is based on astronomy, the study of stars, planets, and time. The calendar blends solar and lunar cycles, which means it considers both the sun’s and the moon’s movements. This makes it more accurate for predicting important cultural and religious events.

The Scientific Knowledge Behind the Indian Calendar

            C.K. Raju explains that the Indian calendar is not just about tradition, it’s based on advanced scientific knowledge. Ancient Indian scholars had a deep understanding of astronomy and used this to develop precise methods for tracking time. Precession is a slow change in the direction of the Earth’s axis over time. Ancient Indian astronomers understood this concept long before it was widely recognized in Western science. This knowledge helped them make their calendars more precise over long periods.

We had a good experience in cultivating Palm sprout in Isai Ambalam last year along with school children. Understanding the benefits of Palm sprouts for health, this year we decided to cultivate them on our office campus. On Aug 3, 2024, we collected more than 150 seeds from different areas in Auroville and around the office. We created a bed for planting the seeds which was around 8×3 feet in area and then we sowed seeds on the bed. It may take more than 3 months for these to sprout and then we will harvest it to have a feast.

Here are the few reflections from our team members on their experience in planting Palm seeds:

Ajay:

My name is Ajay. I stand for happiness and self-awareness for myself and others. Last year, we planted palm sprouts at Isaiambalam School with the children, and we cultivated them in large numbers. This time, we planned to plant them in our office garden area. So, we went along with the children from Isaiambalam School and collected palm fruit/seeds for our garden. We planted those seeds in our garden with the help of our colleagues. While doing this activity, I noticed the interest and involvement towards our traditional practices. We will see the results of those seeds in a span of three months.

Sivaguru prasath:

My name is Sivaguruprasath and I stand for courage, full potential, and equanimity for myself and for others. Last year I felt that I hadn’t contributed to collecting and planting seeds for Palm sprout harvesting, but I delighted in and enjoyed eating the sprouts. This year I decided I should participate fully and along with my team collected and planted Palm seeds. Without team effort and planning, it wouldn’t happen at all. From this, I noticed that we are connecting with healthy things in our tradition, and I feel complete and whole being a part of this activity.

The team was really interested and involved planting the seeds; it felt more like a physical activity for us.

Saranya:

Teamwork and Bonding – Working together on planting helped us bond and improve teamwork. It was fun to share tasks and support each other in a different setting from our usual office work.

Environmental Awareness – The activity reminded us of the importance of taking care of the environment. It felt good to do something positive for nature, and it made us more aware of sustainability.

Stress Relief and Well-being – Being outside and doing physical work was a refreshing break from our daily routine. It reduced stress and made us feel more relaxed and happy.

Reflecting Organization Values – This activity showed that our company cares about teamwork, the environment, and employee well-being. It demonstrated our commitment to creating a supportive and engaged workplace.

Arunkumar:

My name is Arunkumar, and I stand for peace and equity for myself and others. I supported the Isai Ambalam children in collecting and sowing palm seeds for the second consecutive year. As part of C3SLD, where we have been growing some vegetables and flowers around the campus, we decided to plant the palm seeds. We started with only four members, and as we continued, it inspired others to commit to action, which led to the entire process of bed making and placing the palm seeds above it within a time span of 2 hours. The learning from this is that any complex issue can be solved if there is group commitment.

Rajesh:

My name is Rajesh, and I stand for care and integrity for myself and others. While seeding palm seeds for palm sprouts, I noticed that what we have been doing at school with children has become normative for us. That is why we took the initiative to do it at our office. I could see the bigger picture: of taking the importance of palm trees our homes, and community.

What we think are small actions may seem small, but each new initiative we undertake at Isai Ambalam School is something big and good for society.

Pratap:

The palm seed planting activity with the team member was successful done in the last week. I saw the team work while making the bed and collecting palm seeds. It served as a reminder of the importance of taking time for nature and each other, even in a busy office environment. I look forward to watch the palms grow and engaging in more such meaningful activities in the future.

Vasanth:

I am able to connect with what we learned in school by working with children to collect palm fruit and make palm sprouts. I helped with digging, which provided some physical exercise for me. I also noticed the group coordination and teamwork involved. We split into two groups to collect the palm fruits, dug the soil, and sowed the seeds. From this, I learned how to strive for a self-sustainable life by understanding the interdependence within a system and the value of working together to achieve sustainability.

Poonguzhali:

My name is Poonguzhali. I stand for courage for myself and others. When I contributed to planting palm seeds at STEM Land, I could see my value. This was a new experience for me where I could push myself to do more. By participating in the planting of palm seeds, I came to know more about the benefits of our tradition. By setting this up, I noticed the collaboration of our team and their full potential towards it. I also noticed full involvement, courage, perseverance, and teamwork.

NithyaSandhosh:

My name is Nithyasandhosh. I stand for kindness and equality for myself and others. When I was palm seeding, I noticed I was excited and happy to be working with my team mates again after a long time doing this type of hard physical activity. As I waited for the first green sprout to emerge, it was satisfying. It was a powerful reminder that with consistent care, kindness and patience, even the slowest progress can bring great reward.

-Mathegramming Team

A five day Science Technology Engineering Arts and Maths (STEAM) Camp was organised by all the Auroville schools from 27th May to 31st May to inspire and engage young children in STEAM activities. Children participated in STEM activities over a course of five days at different venues. STEM Land introduced children to electronics, Makey Makey, games, puzzles, programming, and craft work. Each day 25 children between the ages of 6 to 13+ from different schools in Auroville came to STEM Land.

We began the sessions by talking about the link between universal values (Monica Sharma, 2017) and technology, as the two are often assumed to be on opposite ends. We used examples of instances when technology was used constructively versus destructively to enable children to imagine the numerous ways in which technology can be imbibed with values. Sessions began with “Stand and Fear” a tool used in Radical Transformational Leadership to recognise our universal values and harness them to manage our fears.

The students were divided in five groups, and they were asked to think about a person they admire most, someone they look up to but not from their immediate circles, – maybe a character from a film, a celebrity etc. children were then asked to think about the qualities in that person that inspire them. The children began to think about their values and what they stand for. Then they shared their thoughts with their partners. The session closed with children affirming their universal values and sharing their insights about what they got to learn about themselves, children shared that this exercise made them feel proud and confident.

Hands-on Activities with Makey-Makey

After the leadership session, we divided the team into five groups. The children were introduced to Makey-Makey, before the session began children were asked to collect leaves or other conducting materials from the school campus. Children were not only excited but also curious to know why they were doing so. After the children got back to the classroom, the Mathegramming team explained how Makey-Makey works – the kit allows users to connect conducting materials like leaves, vegetables, water, etc. to the computer functions of arrow keys, mouse and space-bar using crocodile clips. When those objects are touched, they send signals to the computer, producing different sounds or elicit other responses (such as increase in the size of the sprite on Scratch) depending on the programs we put in Scratch.

Understanding Makey Makey

Basic Components: We showed the children the main components of the Makey Makey kit, including the circuit board, crocodile clips, and USB cables.

How It Works: We explained the concept of conductivity and how Makey Makey uses this principle to turn objects into touchpads. Children learned how to connect Makey Makey to a computer and set it up to work with different software programs.

Hands-On Activities with Makey Makey: Each group worked on a different Makey Makey project. Below are the highlights:

1. Banana Piano

 We connected alligator (crocodile) clips to bananas, each representing a different piano key. Using a Scratch program, we mapped each banana to a musical note.The children played their banana pianos, creating tunes by tapping the fruit. This activity was not only fun but also a great introduction to basic programming.

2. Dancing Console

We created a dance mat using foil and paper, connected to Makey Makey. The children programmed a dancing game where stepping on different parts of the mat would show different dance moves on the screen. The children took turns showing off their dance skills.

Additionally children also participated in the following activities:

• Games and Puzzles: children played many games and puzzles that helped them enhance their critical thinking and collaboration skills.

• Scratch Programming: Kids learned the basics of coding using Scratch, creating their own animations and simple games. This activity helped them think logically and apply their thinking.

• Math Materials: Children also explored math materials like Dienes blocks and fraction kits, they were briefly introduced to how these materials can enhance their understanding of mathematical concepts.

• Kirigami: Similar to Origami, kirigami is also a Japanese art that creates three dimensional designs. It helps them to understand how different folds and cuts can turn into 3D creations.

Conclusion

While children enjoyed the STEAM Camp, they were struck by wonder looking at how Makey-Makey works, everytime children were introduced to Makey-Makey at least one child in the group expressed their wonder using “How cool is that!”. As adults who want to instill values of collaboration in children, we at STEM Land were moved by how compassionate, responsible and fair children were when exploring materials including Makey-Makey, they all ensured that each child in the group is getting a chance to explore the materials.

The children were excited and inspired to adopt a new perspective about technology. We are looking forward to having more such sessions to continue sparking curiosity and creativity in young minds. 

• IlakyaArasi, soundhariya, Premkumar, Dinesh, Preethi and SandhiyaBala

The Mathegramming team visited Kanyakumari to conduct a three-day capacity building workshop with the teachers at Infant Jesus Girls High School in Mulagumoodu. The aim of the workshop was to engage with the teachers and help them understand how they can change the pedagogy of mathematical concepts by using materials and visualizing the metacognitive process adopted in solving math problems, and engaging in interactive storytelling. Additionally, the workshop also focused on building leadership skills in the teachers using Radical Transformational Leadership Tools (RTL) (Monica Sharma, 2017).

Day one opened with an introduction to help the teachers understand the context of Mathegramming, what we do, and who we are. We introduced ourselves using our universal values which made the teachers curious about the same. The introduction was followed by a session on using the Stand & Fear Tool where the teachers identified and enquired about their own universal values and how they can harness them to face their fears. After this brief induction on Mathegramming and our core values we proceeded to mathematical concepts.

The first session revolved around identifying patterns in numbers and how they change when added, subtracted, multiplied and divided, the same was done by visually showing these concepts using materials like the Cuisenaire Rods, Dienes Blocks and Ganith Rack. Multiplication of numbers was shown by the concept of area method using Dienes Blocks. We started with primary concepts to help the teachers get comfortable with the concept of visualization, this was done because basic clarity of the concept will help them deal with higher level concepts in higher grades.

In the afternoon the teachers were introduced to the four profiles i.e., an RTL Tool to understand different parts of our identities. While closing on day one the teachers came to share their insight about all the tools and activities they learned.

The second day started with two minute stillness and focused attention on breathing, then we introduced Deep Listening and Background Conversations to the teachers. The session incorporated time for reflection so that teachers can reflect on the past and apply what they learnt to think about what they could have done differently. This was followed by a session introducing square numbers using Dienes Blocks and square roots of perfect square numbers by understanding the pattern behind the square numbers.

We introduced addition and subtraction of integers using the Othello tokens. In the afternoon they learnt about System Principles (RTL) by watching a short film titled the Story of Stuff. After closing System Principles, we moved to visually explaining the concept of fractions using the fraction kit. Afterwards teachers were given time to explore the scratch projects related to the concepts they learnt about in the past two days, developed by the Mathegramming team. They were interested in showing theseprojects to their students. The day closed with four reflections.

 by the teachers highlighting the usefulness of background conversation and deep listening. Teachers also shared that they liked the concept of opening a session with two minute stillness and adding thought breaks. They are motivated to adopt the same in their practice with the students.

The last day began with the two minute stillness followed by introducing the Conscious Full Spectrum Response Model (CFSR). The teachers struggled to fill the sheet as it demanded them to think about different areas. We encouraged them to come up with an idea to fill the CFSR model using the examples from our own CFSR sheets.

After we closed the session on CFSR sheets we moved on to explore how to visualize decimal numbers and how to multiply decimal numbers visually. At first, they were hesitant and thought that multiplying following the usual method would be better, but afterwards they realized how their students could benefit from this technique. Then we introduced algebraic equations using weighing balance and algebraic tiles to differentiate the confusing terms. They all worked on the algebraic tiles on how to show different terms in their class. They liked the visual idea of the algebraic tiles and how to make them.

In the afternoon, we reconnected with RTL tools and explained about the three types of complaints. Then, we explored concepts of electronics such as resistance and how it works. We started with measuring our body resistance using the multimeter, then measured the body resistance with ultrasound gel. Then we explained how our body resistance plays a role in lighting up the LED light with a 9V battery.

Since the sessions were delivered in Tamil, the concepts were easily understood by the teachers and did not daunt them. The teachers had never thought of teaching Mathematics visually, they were inspired to do it with their students now. However, the teachers much like the students were hesitant in coming up and sharing their learnings but after doing this a few times they got comfortable with the process we adopted, and voluntarily came and shared their insights.

Mathegramming team is grateful for the opportunity to hold this session with the teachers and create a change in how mathematics is taught. It directly impacts our growth and pushes us outside of our comfort zones. We look forward to more such opportunities in the future.

Reflections:

My name is Premkumar I deeply care about courage and equality for myself and others. I have learnt that I can do more and I can change many things if I want to change. It was a nice journey with the teachers and I am looking forward for many events like this to develop my learning and give something valuable to others to make their life better.

My name is Soundhariya. I deeply care about courage for myself and for others. It was a great opportunity for me to work with the teachers. They were excited and curious to learn about mathematics and electronics and how these subjects are used in our daily lives. They shared their thoughts with the group while working on the RTL session and mathematical concepts. The session created values of equality, responsibility, and reaching our full potential.

My name is Dinesh. I stand for care and perseverance for myself and others. It was a new experience for me to train the teachers, and I had a great chance to share my learnings with them. On the first day of the session, I was the PC for my table and initially acted from my fear(judgment). I answered their questions and guided them on how to do the exercise, which brought confidence in me. I noticed that I acted from my stand, not from my fears. I realized that courage is not the absence of fear, but the ability to act in spite of fear.

My name is Preethi. I stand for courage and kindness for myself and others.  It was a wonderful experience to work with teachers and get to share my learnings with them. When I work with teachers, I get to recognize areas where I can grow and develop my skills. I learnt how to be creative so that I can make them engage and understand the concept. It built confident in me to teach them effectively.

My name is IlakyaArasi. I stand for patience and courage for myself and others. I learned that training the teachers-to encourage them to do things differently, to make them act out from their comfortable space is a challenging work. This journey made me reflect to prepare myself differently for the further opportunities.

My name is Sandhiya Bala. I stand for courage, care, and happiness for myself and others. It was a new experience for me to teach the RTL (Stewardship tools) to teachers, and I had a great opportunity to share my learnings with them. It removed my fear while conducting the session with them. Personally, it gave me a chance to reflect on many aspects of my life, such as my career. I noticed that I acted from my values (universal values) while teaching the tools, and I learned how to manage work-life balance. It has built my confidence to teach them effectively

-Ilkaya(Mathegramming Team)

The Mathegramming team’s partnership with Vaasavi school children resulted in a series of interactive and innovative Scratch mathematical projects, which enriched the learning experience and logical thinking of the children. The work started on September 12, 2023 to February 15, 2024 for the 7th graders. Scratch was introduced to the students in the way of making games, drawing shapes and asking questions which induced their creativity, thinking and the sense of building.

After that it was moved to math concepts like Fractions, integers, decimal multiplication, algebra and simple interest with visualization. Each concept was visualized in a specific way that students could learn the concepts well and explore in a creative way. Since it takes time work on the math project from scratch, we made some core modules for each topic that they could build on and make their own projects. A scratch account was created for each four classes. Then, students logged in with their class account and used the modules to create the projects with our help.

Shifts:

1. Transforming students from rote learning to visual learning of mathematical concepts that fosters curiosity, innovation and lifelong learning

2. Not challenging students to challenging the students with creative tasks to make their learning more interesting.

3. Low confidence in bringing out confidence in every student.

4. From no access to programming to access to programming platforms integrated with mathematics and making a space where students can be at their full potential.

Fractions were visualized using the circles. When the module was given to the students, they were asked to explore it and do what fun things they can do with it before going into the concept of fraction.

Here are some of the projects children made with the module on drawing a fraction as a circle

Decimal Multiplication was done using the area of the rectangle concept. Since, the module for this is easy to make instead of using the old module. Students learned to create their own module with the help of the team. First, they observed the blocks and found the pattern and the variables to make their own blocks.

https://scratch.mit.edu/projects/957761814

Integers were taken using two colored tokens one color for positive integers and other for negative integers.

In scratch, there is a student-teacher account facility available. With a teacher account, the  teacher can enroll many students to their class and create separate accounts for each student. The teacher can also post the update of their class, links for the required materials and can monitor each student’s activities.

Algebraic terms were introduced as each term is an area of a rectangle or a square. This method is particularly to help students to identify the like and unlike terms using different colors and lengths for each variable. This really helped the students to understand that ‘x’ and ‘’ are two different terms even though they have the same variable.

Simple interest was shown using the bar graph.

Learning scratch also inspired students to build their own fun projects not only on math projects but on fun interactive games.

Reflections:

My name is Dinesh. I stand for care and perseverance for myself and for others. While teaching Vasavi children I noted that I gave the students what I have expected in my school life, as I wanted to learn mathematics, programming in a logical way rather than mugging up. As a stem teacher I contribute my best to the Vaasavi students and I made them think logically from scratch and gave the problem statement and asked students to solve the problem statement on their own. With that some students were able to find the logic and who were not at that time, peer learning went well. Students helped each other and helped their friends to find the logic, I saw the quality of care in the students.

My name is Premkumar. I deeply care about courage and equality for myself and others. While working with Vaasavi children I learnt that I can add some value to the student’s Education. It is a big group of students which was challenging in the beginning and after it became easy to work with them and the students were very enthusiastic about learning new things and learning mathematics in a different way which boosted my confidence to work with them.

I have learnt many things in this journey and I have practiced deep listening throughout the process and I am able to see the commitment behind complaints and I am able to see the distinction between business as usual and acting from my full potential. It was also a learning journey for me also and I am grateful to work with Students.

My name is Soundhariya, and I stand for courage for myself and others. When I worked with the students of Vaasavi International School, I introduced a new way of learning math concepts through the Scratch program. In the traditional method of teaching math, students often felt difficult and disconnected. However, our Mathegramming approach filled this gap by creativity and logic of programming. The students showed great excitement while engaging with the Scratch program, and our team found themselves inspired by their curiosity and eagerness to learn. Working with the students was a fantastic experience for the Mathegramming team and the school management.

My name is Preethi. I stand for courage, kindness and perseverance for myself and others. For many kids including me when I was kid, math is a scary and confusing subject. The methods I learnt often involved lots of memorization and worksheets, which made me hate math. But in Vaasavi school we taught children math concepts with materials and did projects from scratch  With this method they learnt math more excitingly. Instead of just remembering math rules, they really get what they’re doing. Through Scratch projects, they learnt to think critically and logically as they debug their code and figure out how to make their programs work just right. While they were working on the project, they worked together and encouraged each other and helped each other out when they got struck somewhere. It built important skills like problem-solving and teamwork, and most importantly, it empowered them to become confident and creative thinkers. When we taught them math differently I saw changes in them, they were more engaged and confident in what they learnt. It made me feel that I’m making a shift and I feel accomplished.

My name is Sivashankaran. I stand for equality for myself and others. When teaching visual math, the way we teach and the things we use in class change. Instead of just talking and writing on the board, we do more activities where students get to draw and work with pictures to solve problems.