Stellar Exploratory Data Analysis or How to create the HR Diagram with R

 

I recently have started to refresh my skills with R programming language. I am doing the  Harvard Course on Data Science on EdX. I am using R Studio for doing all the exercises. In the second part of the course, Visualisation, which is an area of research interest for me, there is an exercise on stars dataset. But this exercise was available only to those who were crediting the course. Since I was not crediting, but only auditing I left the exercise as it is. But after a week or so I looked at the stars dataset. And thought I should do some explorations on this. For this we have to load the R package dslabs specially designed for this course. This post is detailing the exploratory data analysis with this dataset. (Disclaimer: I have used help from ChatGPT in writing this post for both content and code.)

> library(dslabs)

Once this is loaded, we load the stars dataset

data(stars)

Structure of the dataset

To understand what is the data contained in this data set and how is it structured we can use several ways. The head(stars) command will give use first few lines of the data set.

> head(stars)
star magnitude temp type
1 Sun 4.8 5840 G
2 SiriusA 1.4 9620 A
3 Canopus -3.1 7400 F
4 Arcturus -0.4 4590 K
5 AlphaCentauriA 4.3 5840 G
6 Vega 0.5 9900 A

While the  tail(stars) gives last few lines of the data set

tail(stars)
star magnitude temp type
91 *40EridaniA 6.0 4900 K
92 *40EridaniB 11.1 10000 DA
93 *40EridaniC 12.8 2940 M
94 *70OphiuchiA 5.8 4950 K
95 *70OphiuchiB 7.5 3870 K
96 EVLacertae 11.7 2800 M

To understand structure further we can use the str(stars) command

> str(stars)
'data.frame': 96 obs. of 4 variables:
$ star : Factor w/ 95 levels "*40EridaniA",..: 87 85 48 38 33 92 49 79 77 47 ...
$ magnitude: num 4.8 1.4 -3.1 -0.4 4.3 0.5 -0.6 -7.2 2.6 -5.7 ...
$ temp : int 5840 9620 7400 4590 5840 9900 5150 12140 6580 3200 ...
$ type : chr "G" "A" "F" "K" ...

In RStudio we can also see the data with View(Stars) function in a much nicer (tabular) way. It opens up the data in another frame as shown below.

Thus we see that it has 96 observations with four variables, namely star, magnitude, temp and type. The str(stars) command also tells use the datatype of the columns, they are all different: factor, num, int, chr. Let us understand what each of the column represents.

Name of stars

The star variable has the names of the stars as seen in the table above. Many of the names are of ancient and mythological origins, while some are modern. Most are of Arabic origin, while few are from Latin. Have a look at Star Lore of All Ages by William Olcott to know some of the mythologies associated with these names. Typically the alphabets after the star names indicate them being part of a stellar system, for example Alpha Centauri is a triple star system. The nomenclature is such that A represents the brightest member of the system, B the second brightest and so on. Also notice that some names have Greek pre-fixes, as in the case of of Alpha Centauri. This Greek letter scheme was introduced by Bayer in 1603 and is known as Bayer Designation. The Greek letters  denote the visual magnitude or brightness (we will come to the meaning of this next) of the stars in a given constellation. So Alpha Centuari would mean the brightest star in the Centaurus constellation. Before invention of the telescope the number of stars that are observable were limited by the limits of human visual magnitude which is about +6. With invention of telescope and their continuous evolution with increasing light gathering power, we discovered more and more stars. Galileo is the first one to view new stars and publish them in his Sidereal Messenger. He shows us that seen through the telescope, there are many more stars in the Pleiades constellation than can be seen via naked eyes (~+6 to max +7 with about 4200 stars possibly visible).

Soon, so many new stars were discovered that it was not possible to name them all. So coding of the names begun. The large telescopes which were constructed would do a sweep of the sky using big and powerful lenses and would create catalogue of stars. Some of the names in the data set indicate these data sets, for example HD denotes Henry Draper Catalogue.

Magnitudes of stars

Now let us look at the other three columns present us with observations of these stars. Let us understand what they mean. The second column represents magnitude of the stars. The stellar magnitude is of two types: apparent and absolute. The apparent magnitude is a measure of the brightness of the star and depends on its actual brightness, distance from us and any loss of the brightness due to intervening media. The magnitude scale was devised by Claudius Ptolemy in second century. The first magnitude stars were the brightest in the sky with sixth being the dimmest. The modern scale follows this classification and has made it mathematical. The scale is reverse logarithmic, meaning that lower the magnitude, brighter is the object. A magnitude difference of 1.0 corresponds to a brightness ratio of $ \sqrt[5]{100} $ or about 2.512. Now if you are wondering why the magnitude scale is logarithmic, the answer lies in the physiology of our visual system. As with the auditory system, our visual system is not linear but logarithmic. What this means is that if we perceive an object to be of double brightness of another object, then their actual brightness (as measured by a photometer) are about 2.5. This fact is encapsulated well in the Weber-Fechnar law. The apparent magnitude of the Sun is about -26.7, it is after all the brightest object in the sky for us. Venus, when it is brightest is about -4.9. The apparent magnitude of Neptune is +7.7 which explains why it was undiscovered till the invention of the telescope.

But looking at the table about the very first entry lists Sun’s magnitude as +4.8. This is because the dataset contains the absolute magnitude and not the apparent magnitude. Absolute magnitude is defined as “apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs (32.6 light-years), without dimming by interstellar matter and cosmic dust.” As we know, the brightness of an object is inversely proportional to square of the distance (inverse square law). Due to this fact very bright objects can appear very dim if they are very far away, and vice versa. Thus if we place the Sun at a distance of about 32.6 light years it will be not-so-bright and will be an “average” star with magnitude +4.8. The difference in these two magnitudes is -31.57 and this translates to huge brightness difference of 3.839 $\times$ 1012. And of course this  definition does not take into account the interstellar matter which further dims the stars. Thus to find the absolute magnitude of the stars we also need to know their distance. This is possible for some nearby stars for which the parallax has been detected. But for a vast majority of stars, the parallax is too small to be detected because they are too faraway. The distance measure parsec we saw earlier is defined on basis of parallax, one parsec is the distance at which 1 AU (astronomical unit: distance between Earth and Sun) subtends an angle of one arcsecond or 1/3600 of a degree.

Thus finding distance to the stars is crucial if we want to know their actual magnitudes. For finding the cosmic distances various techniques are used, we will not go into their details. But for our current purpose, we know that the stars dataset has absolute magnitudes of stars. The range of magnitudes in the dataset is

> range(stars$magnitude)
[1] -8 17

Thus stars in the dataset have a difference of 25 magnitudes, that is a brightness ratio of 105! Which are these brightest and dimmest stars? And how many stars of each magnitude are there in the data set? We can answer these type of questions with simple queries to our dataset. For starters let us find out the brightest and dimmest stars in the dataset. Each row in the dataset has an index, which is the first column in the table from RStudio above. Thus if we were to write:

> stars[1]

it will give us all the entries of the first column,

star
1 Sun
2 SiriusA
3 Canopus
4 Arcturus
5 AlphaCentauriA
6 Vega
7 Capella
8 Rigel
9 ProcyonA
10 Betelgeuse
...
...

But if we want only a single row, instead of a column, we have to tell that by keeping a , in the index 1. Thus for the first row we write

> stars[1,]
> star magnitude temp type
1 Sun 4.8 5840 G

Thus to find the brightest or dimmest star we will have to find its index and then we can find its name from the corresponding column. So how do we do that? For this we have functions which.max and which.min, we use them thus:

> which.max(stars$magnitude)
[1] 76

We feed this to the dataset and get

> stars[76,]
star magnitude temp type
76 G51-I5 17 2500 M

This can also be done in a single line

> stars[which.min(stars$magnitude), ]
star magnitude temp type
45 DeltaCanisMajoris -8 6100 F

Now let us check the distribution of these magnitudes. The simplest way to do this is to create a  histogram using the hist function.

hist(stars$magnitude)

This gives the following output

As we can see it has by default binned the magnitudes in bins of 5 units and the distribution here is bimodal with one peak between -5 and 0 and another peak between 10 and 15. We can tweak the width of the bars to get a much finer picture of the distribution. For this hist function has option to add breaks manually. We have used the seq function here ranging from -10 to 20 in steps of 1.

> hist(stars$magnitude, breaks = seq(-10, 20, by = 1))

And this gives us:

Thus we see that the maximum number of stars (9) are at -1 magnitude  and three magnitudes have one star each while +3 magnitude doesn’t have any stars. This histogram could be made more reader friendly if we can add the count on the bars. For this we need to get some coordinates and numbers. We first get the counts

mag_data <- hist(stars$magnitude, breaks = seq(-10,20, 1), plot = FALSE)

This will give us the actual number of counts

> [1] 0 1 2 1 7 6 4 3 3 9 6 4 4 0 2 5 2 2 2 1 5 7 3 7 5 3 2 0 0 0

Now to place them at the middle of the bars of histogram we need midpoints of the bars, we use mag_data$mids to find them and mag_data_counts for the count for labels.

> text(mag_data$mids, mag_data$counts, labels = mag_data$counts, pos = 3, cex = 0.8, col = "black")

To get the desired graph

Thus we have a fairly large distribution of stellar magnitudes.

Now if we ask ourselves this question How many stars in this dataset are visible to the naked eye? What can we say? We know that limiting magnitude for naked eye is +6. So, a simple query should suffice:

count(stars %>% filter(magnitude <= 6))
n
1 57

(Here we have used the pipe function %>% to pass on data from one argument to another from the dplyr pacakge. This query shows that we have 57 stars which have magnitude less than or equal to 6. Hence these many should be visible… But wait it is the absolute magnitude that we have in this dataset, so this question itself cannot be answered unless we have the apparent magnitudes of the stars. Though computationally correct, this answer has no meaning as it is cannot be treated same as the one with apparent magnitude which we experience while watching the stars.

Temperature of Stars

The third column in the data set is the temp or the temperature. Now, at one point in the history of astronomy people believed that we would never be able to understand the structure or the content of the stars. But the invention of spectroscopy as a discipline and its application to astronomy made this possible. With the spectroscope applied to the end of the telescope (astronomical spectroscopy), we could now understand the composition of the stars, their speed and their temperature. The information for the composition came from the various emission and absorption lines in the spectra of the stars, which were then compared with similar lines produced in the laboratory by heating various elements. Helium was first discovered in this manner: first in the spectrum of the Sun and then in the laboratory. For detailed story of stellar spectroscopy one can see the book Astronomical Spectrographs and Their History by John Hearnshaw. Though an exact understanding of the origin of the spectral line came only after the advent of quantum mechanics in early part of 20th century.

But the spectrum also tells us about the surface temperature of the stars. How this is so? For this we need to invoke one of the fundamental ideas in physics: the blackbody radiation. Now if we find the intensity of radiation from a body at different wavelengths (or frequencies) we get a curve. This curve is typical and for different temperatures we get unique curves (they don’t intersect). Of course this is true for an ideal blackbody which is an idealized opaque, non-reflective body. Stellar spectrum is like that of an ideal blackbody,  this continuous spectrum is punctuated with absorption and emission lines as shown in the book cover above.

The frequency or wavelength at which the radiation has maximum intensity (brightness/luminosity) is related to the temperature of the body, typical curves are shown as above. Stars behave almost as ideal black bodies. Notice that as the temperature of the body increases the peak radiation wavelength increases (frequency is reduced) as shown in the diagram above. These relationships are given by the formula

$$
L = 4 \pi R^{2} \sigma T^{4}
$$

where $L$ is the luminosity, $R$ is the radius, $\sigma$ is Stephan’s constant and $T$ is the temperature. This equation tells us that $L$ is much more dependent on the $T$, so hotter stars would be more brighter.

It was failure of the classical ideas of radiation and thermodynamics to explain the nature of blackbody radiation that led to formulation of quantum mechanics by Max Planck in the form of Planck’s law for quantisation of energy. For a detailed look at the history of this path breaking episode in history of science one of the classics is Thomas Kuhn’s Black-Body Theory and the Quantum Discontinuity, 1894—1912.

That is to say hotter bodies have shorter peak frequencies. In other words, blue stars are hotter than the red ones. (Our hot and cold symbolic colours on the plumbing peripherals needs to change: we have it completely wrong!) Thus the spectrum of the stars gives as its absolute temperature, along with all other information that we can obtain from the stars. The spectrum is our only source of information for stars. This is what is represented in the third column of our data. For our dataset the range of stellar temperatures we have a wide range of temperatures.

range(stars$temp)
[1] 2500 33600

Let us explore this column a bit. If we plot a histogram with default options we get:

> hist(stars$temp)

This is showing maximum stars have a temperature below 10000. We can bin at 1000 and add labels to get a much better sense. Which star has 0 temperature??

hist(stars$temp, breaks = seq(0,35000, 1000))
> temp_data <- hist(stars$temp, breaks = seq(0,35000, 1000), plot = FALSE)
> text(temp_data$mids, temp_data$counts, labels = temp_data$counts, pos = 3, cex = 0.8, col = "black")

This plot gives us much better sense of the distribution of stellar temperatures. With most of the temperatures being in 2000-3000 degrees Kelvin range. The table() function also provides useful information about distribution of temperatures in the column.

> table(stars$temp)

2500 2670 2800 2940 3070 3200 3340 3480 3750 3870 4130 4590
1 10 7 5 1 3 4 1 1 2 3 3
4730 4900 4950 5150 5840 6100 6580 6600 7400 7700 8060 9060
1 5 1 2 2 2 1 1 2 1 2 1
9300 9340 9620 9700 9900 10000 11000 12140 12400 13000 13260 14800
1 2 3 1 4 1 1 1 1 1 1 1
15550 20500 23000 25500 26950 28000 33600
1 4 2 5 1 2 1

While the summary() function provides the basic statistics:

> summary(stars$temp)
Min. 1st Qu. Median Mean 3rd Qu. Max.
2500 3168 5050 8752 9900 33600

Type of Stars

The fourth and final column of our data is type. This category of data is again based on the spectral data of stars and is type of spectral classification of stars. “The spectral class of a star is a short code primarily summarizing the ionization state, giving an objective measure of the photosphere’s temperature. ” The categories of the type of stars and their physical properties are summarised in the table below. The type of stars and their temperature is related, with “O” type stars being the hottest, while “M” type stars are the coolest. The Sun is an average “G” type star.

There are several mnemonics that can help one remember the ordering of the stars in this classification. One that I still remember from by Astrophysics class is Oh Be A Fine Girl/Guy Kiss Me Right Now. Also notice that this “type” classification is also related to size of the stars in terms of solar radius.

In our dataset, we can see what type of stars we have by

> stars$type
[1] "G" "A" "F" "K" "G" "A" "G" "B" "F" "M" "B" "B" "A" "K"
[15] "B" "M" "A" "K" "A" "B" "B" "B" "B" "B" "B" "A" "M" "B"
[29] "K" "B" "A" "B" "B" "F" "O" "K" "A" "B" "B" "F" "K" "B"
[43] "B" "K" "F" "A" "A" "F" "B" "A" "M" "K" "M" "M" "M" "M"
[57] "M" "A" "DA" "M" "M" "K" "M" "M" "M" "M" "K" "K" "K" "M"
[71] "M" "G" "F" "DF" "M" "M" "M" "M" "K" "M" "M" "M" "M" "M"
[85] "M" "DB" "M" "M" "A" "M" "K" "DA" "M" "K" "K" "M"

Our Sun is G-type star in this classification (first entry). If we use the table() function on this column we get the frequency of each type of star in the dataset.

> table(stars$type)

A B DA DB DF F G K M O
13 19 2 1 1 7 4 16 32 1

And to see a barplot of this table we will use ggplot2() package. Load the package using library using library(ggplot2) and then

> stars %>% ggplot(aes(type)) + geom_bar() + geom_text(stat = "count", aes(label = after_stat(count)), vjust = -0.5, size = 4)

Thus we see that “M” type stars are the maximum in our dataset. But we can do better, we can sort this data according the frequency of the types. For this we use the code:

> type_count <- table(stars$type) > # count the frequencies
> sorted_type <- names(sort(type_count)) > # sort them
> stars$type <- factor(stars$type, levels = sorted_type) > # reorder them with levels and plot them
> stars %>% ggplot(aes(type)) + geom_bar(fill = "darkgray") + geom_text(stat = "count", aes(label = after_stat(count)), vjust = -0.5, size = 4)

And we get

To plot HR Diagram

Now, given my training in astronomy and astrophysics, the first reaction that came to my mind after seeing this data was this is the data for the HR Diagram! The HR diagram presents us with the fundamental relationship of types and temperature of stars. This was an crucial step in understanding stellar evolution. The intials HR stand for the two astronomers who independently found this relationship: The diagram was created independently in 1911 by Ejnar Hertzsprung and by Henry Norris Russell in 1913.

By early part of 20th century several star catalogues had been around, but nothing stellar evolution or structure was known. The stellar spectrographs revealed what elements were present in the stars, but the energy source of the stars was still an unresolved question. Classical physics had no answer to this fundamental question about how stars were able to create so much energy (for example, see Stars A Very Short Introduction by James Kaler on the idea that charcoal powers the Sun by Lord Kelvin). Added to this was the age of the stars, from geological data and idea of geological deep time, the Sun was estimated to be 4 billion years old as was the Earth. So stars had been producing so much energy for such a long time! But that is not the point of this post, the HR diagram definitely helped the astronomers think about the idea that stars might not be static but evolve in time. The International Astronomical Union conducted a special symposium titled The HR Diagram in 1977. The proceedings of the symposium have several articles of interest on the history of creation and interpretation of the HR Diagram.

I think it was but natural that astronomers tried to find correlations between various properties of thousands of stars in these catalogues. And when they did they find a (co-)relationship between them. The HR diagram exists in many versions, but the basic idea is to plot the absolute magnitude and temperature (or colour index). Let us plot these two  to see the co-relation, for this we again use the ggplot2() pacakge and its scatterplot function geom_point().

> stars %>% ggplot(aes(temp, magnitude)) + geom_point()

This gives us the basic plot of HR diagram.

Immediately we can see that the stars are not randomly scattered on this plot, but are grouped in clusters. And most of them lie in a “band”. Though there are outliers at the lower temperature and magnitude range and high magnitude and temperature around 10-15 thousand range. We see that most stars lie in a band which is called the “Main Sequence”. We can try to fit a function here in this plot using some options in the ggplot() library, we use geom_smooth() function for this and get:

stars %>% ggplot(aes(temp, magnitude)) + geom_point() + geom_smooth( se = FALSE, color = “red”)

Of course this smooth curve is a very crude (perhaps wrong?) approximation of the data, but it certainly points us towards some sort of correlation between the two quantities for most of the stars. But wait, we have another categorical variable in our dataset, the type of stars. How are the different types of stars distributed on this curve? For this we introduce type variable in the aesthetics argument of ggplot() to colour the stars on our plot according to this category:

> stars %>% ggplot(aes(temp, magnitude, color = type)) + geom_smooth( se = FALSE, color = "red") + geom_point()

This produces the plot

Thus we see there is a grouping of stars by the type. Of course the colours in the palette here are not the true representatives of the star colours. The HR diagram was first published around 1911-13, when quantum mechanics was in its nascent stages. The ideas of Rutherford’s model were still extant and was just out. The fact that this diagram indicated a relationship between the magnitude and temperature, led to thinking about stellar structure itself and its ways of producing energy with fundamentally new ideas about matter and energy from quantum mechanics and their transformation from relativistic physics. But that is a story in future. For now, let us come to our HR diagram. From the dataset we have one more variable, the star name which could be used in this plot. We can name all the stars in the plot (there are only 96). For this we use the geom_text() function in ggplot()

> stars %>% ggplot(aes(temp, magnitude, color = type), label = star) + geom_smooth( se = FALSE, color = "red") + geom_point() + geom_text((aes( label = star)), nudge_y = 0.5, size = 3)

This produces a rather messy plot, where most of the starnames are on top of each other and not readable:

To overcome this clutter we use another package ggrepel() with the following code:

> stars %>% ggplot(aes(temp, magnitude, color = type), label = star) + geom_smooth( se = FALSE, color = "red") + geom_text_repel(aes(label = star))

This produces the plot with the warning "Warning message: ggrepel: 13 unlabeled data points (too many overlaps). Consider increasing max.overlaps ". To overcome this we increase the max.overlaps to 50.

> stars %>% ggplot(aes(temp, magnitude, color = type), label = star) + geom_point() + geom_smooth( se = FALSE, color = "red") + geom_text_repel(aes(label = star), max.overlaps = 50)

 

This still appears cluttered a bit, scaling the plot while exporting gives this plot, though one would need to zoom in to read the labels.

Of course with a different data set, with larger number and type of stars we would see slightly different clustering, but the general pattern is the same.

We thus see that starting from the basic data wrangling we can generate one of the most important diagrams in astrophysics. I learned a lot of R in the process of creating this diagram. Next task is to

How big is the shadow of the Earth?


The Sun is our ultimate light source on Earth. The side of the Earth facing the Sun is bathed in sunlight, due to our rotation this side changes continuously. The side which faces the Sun has the day, and the other side is the night, in the shadow of the entire Earth. The sun being an extended source (and not a point source), the Earth’s shadow had both umbra and penumbra. Umbra is the region where no light falls, while penumbra is a region where some light falls. In case of an extended source like the Sun, this would mean that light from some part of the Sun does fall in the penumbra.  Occasionally, when the Moon falls in this shadow we get the lunar eclipse. Sometimes it is total lunar eclipse, while many other times it is partial lunar eclipse. Total lunar eclipse occurs when the Moon falls in the umbra, while partial one occurs when it is in penumbra. On the other hand, when the Moon is between the Earth and the Sun, we get a solar eclipse. The places where the umbra of the Moon’s shadow falls, we get total solar eclipse, which is a narrow path on the surface of the Earth, and places where the penumbra falls a partial solar eclipse is visible. But how big is this shadow? How long is it? How big is the umbra and how big is the penumbra? We will do some rough calculations, to estimate these answers and some more to understand the phenomena of eclipses.

We will start with a reasonable assumption that both the Sun and the Earth as spheres. The radii of the Sun, the Earth and the Moon, and the respective distances between them are known. The Sun-Earth-Moon system being a dynamic one, the distances change depending on the configurations, but we can assume average distances for our purpose.

[The image above is interactive, move the points to see the changes. This construction is not to scale!. The simulation was created with Cinderella ]

 

The diameter of the Earth is approximately 12,742 kilometers, and the diameter of the Sun is about 1,391,000 kilometers, hence the ratio is about 109, while the distance between the Sun and the Earth is about 149 million kilometers. A couple of illustrations depicting it on the correct scale.

 

 

The Sun’s (with center A) diameter is represented by DF, while EG represents Earth’s (with center C) diameter. We connect the centers of Earth and Sun. The umbra will be limited in extent in the cone with base EG and height HC, while the penumbra is infinite in extent expanding from EG to infinity. The region from umbra to penumbra changes in intensity gradually. If we take a projection of the system on a plane bisecting the spheres, we get two similar triangles HDF and HEG. We have made an assumption that our properties of similar triangles from Euclidean geometry are valid here.

In the schematic diagram above (not to scale) the umbra of the Earth terminates at point H. Point H is the point which when extended gives tangents to both the circles. (How do we find a point which gives tangents to both the circles? Is this point unique?). Now by simple ratio of similar triangles, we get

$$
\frac{DF}{EG} = \frac{HA}{HC}  = \frac{HC+AC}{HC}
$$

Therefore,

$$
HC = \frac{AC}{DF/EG -1}
$$

Now, $DF/EG = 109$, and $AC$ = 149 million km,  substituting the values we get the length of the umbra $HC \approx$  1.37 million km. The Moon, which is at an average distance of 384,400 kilometers,  sometimes falls in this umbra, we get a total lunar eclipse. The composite image of different phases of a total lunar eclipse below depicts this beautifully. One can “see” the round shape of Earth’s umbra in the central three images of the Moon (red coloured) when it is completely in the umbra of the Earth (Why is it red?).

When only a part of umbra falls on the moon we get a partial lunar eclipse as shown below. Only a part of Earth’s umbra is on the Moon.

So if the moon was a bit further away, lets say at 500,000 km, we would not get a total solar eclipse. Due to a tilt in Moon’s orbit not every new moon is an eclipse meaning that the Moon is outside both the umbra and the penumbra.

The observations of the lunar eclipse can also help us estimate the diameter of the Moon.

Similar principle applies (though the numbers change) for solar eclipses, when the Moon is between the Earth and the Sun. In case of the Moon, ratio of diameter of the Sun and the Moon is about 400. With the distance between them approximately equal to the distance between Earth and the Sun. Hence the length of the umbra using the above formula is 0.37 million km or about 370,000 km. This makes the total eclipse visible on a small region of Earth and is not extended, even the penumbra is not large (How wide is the umbra and the penumbra of the moon on the surface of the Earth?).

When only penumbra is falling on a given region, we get the partial solar eclipse.

You can explore when solar eclipse will occur in your area (or has occurred) using the Solar Eclipse Explorer.

This is how the umbra of the Moon looks like from space.

And same thing would happen to a globe held in sunlight, its shadow would be given by the same ratio.

Thus we see that the numbers are almost matched to give us total solar eclipse, sometimes when the moon is a bit further away we may also get what is called the annular solar eclipse, in which the Sun is not covered completely by the Moon. Though the total lunar eclipses are relatively common (average twice a year) as compared to total solar eclipses (once 18 months to 2 years). Another coincidence is that the angular diameters of the Moon and the Sun are almost matched in the sky, both are about half a degree (distance/diameter ratio is about 1/110). Combined with the ratio of distances we are fortunate to get total solar eclipses.

Seeing and experiencing a total solar eclipse is an overwhelming experience even when we have an understanding about why and how it happens. More so in the past, when the Sun considered a god, went out in broad daylight. This was considered (and is still considered by many) as a bad omen. But how did the ancient people understand eclipses?  There is a certain periodicity in the eclipses, which can be found out by collecting large number of observations and finding patterns in them. This was done by ancient Babylonians, who had continuous data about eclipses from several centuries. Of course sometimes the eclipse will happen in some other part of the Earth and not be visible in the given region, still it could be predicted.   To be able to predict eclipses was a great power, and people who could do that became the priestly class. But the Babylonians did not have a model to explain such observations. Next stage that came up was in ancient Greece where models were developed to explain (and predict) the observations. This continues to our present age.

The discussion we have had applies in the case when the light source (in this case the Sun) is larger than the opaque object (in this case the Earth). If the the light source is smaller than the object what will happen to the umbra? It turns out that the umbra is infinite in extent. You see this effect when you get your hand close to a flame of candle and the shadow of your hand becomes ridiculously large! See what happens in the interactive simulation above.

References

James Southhall Mirrors, Prisms and Lenses (1918) Macmillan Company

Eric Rogers Physics for the Inquiring Mind (1969) Princeton

 

Remarkable Curves 1: The Straight Line and the Circle

 

 

 

 

The Straight Line and the circle

(Note: All the images are interactive, move the points around to see. Dynamic mathematics interactive web page with Cinderella )

A moving point describes a straight line when it passes from one
position to another along the shortest possible path. A straight line
can be drawn with the help of a ruler; when a pencil runs along the
edge of a ruler it leaves a trace on the paper in the form of a
straight line.

When a point moves on a surface at a constant distance from another
fixed point on the same surface it describes a circle. Because of this
property of the circle we are able to draw a circle with the help of
compasses.

The straight line and the circle are the simplest and at the same time
the most remarkable curves as far as their properties are concerned.

You are no doubt more familiar with these two curves than with
others. But you should not imagine that you know all of the most
important properties of straight lines and curves. For example, you
may not know that if the vertices of the triangles $ABC$ and $AB’C’$
lie on three straight lines intersecting at the point $S$ (Fig. 1),
the three points of intersection $M$, $K$, $L$ of the corresponding
sides of the triangles, the sides $AB$ and $A’B’$, $BC$ and $B’C’$,
and $AC$ and $A’C’$, must be collinear, that is, they lie on a single
straight line.

(Note: this image below is interactive, move the points to see the dynamic change!)

You are sure to know that a point $M$ moving in a plane equidistantly
from two fixed points, say $F_1$, and $F_2$, of the same plane, that
is, so that $MF_{1}= MF_{2}$, describes a straight line (Fig. 2).

But you might find it difficult to answer the question:

What type of curve will point $M$ describe if the distance of $M$ from
$F_1$, is a certain number of times greater than that from $F_2$ (for
instance, in Fig. 3 it is twice as great)?

The curve turns out to be a circle. Hence if the point $M$ moves in a
plane so that the distance of $M$ from one of the fixed
points. $F_{1}$ or $F_{2}$, in the same plane is always proportional
to the distance from the other fixed point, that is

$$
MF_{1} = k \times MF_{2}
$$

then $M$ describes either a straight line (when the factor of
proportionality is unity) or a circle (when the factor of
proportionality is other than unity).

 

This is a post to create interactive mathematics elements using Cinderella a Free Software alternative to GeoGebra which is no longer a Free Software. The files have been exported from Cinderella at html interactives)

Preternatural Photographs

A red bloom from Indian summer. This photo has flowers from the Canonball tree, Gulmohar and African Tulip taken by keeping them on a notebook Taken with one of the most basic cameras the Canon A800.

I got my first camera c. 2005. It was the Canon S2 with 12x optical zoom and 5 MP sensor and could support a 1 GB memory card. By today’s standards these specs look very primitive, but this is almost 18 years ago. I have taken several thousand pictures with that camera, resetting the image counter two times. About 2015 the camera sensor gave up, and they could not repair it. The camera, had super zoom for those days, but its macro function was excellent in terms of focusing very well on the macro subjects. Then I got my hands on DSLRs the Sony Alpha 350 and then finally a Nikon D300 with excellent selection of prime lenses. But this post is not about the cameras per se, but the photographs.

The magnificent flower of Epiphyllum oxypetallum (mistaken popularly as bramhakamal), taken with Canon S2.

Among all the photos that I have taken some just stand out from the rest. The light, the focus, the exposure and the framing is just perfect. I don’t know how to explain this aesthetic appeal of these photographs. But in these photos, even amongst a batch of hundreds taken in the same setting or with same subjects, some photos just come out extraordinary as compared to the rest. As a photographer you might have experienced this too.

Sophia College, Mumbai corridor, taken with Nikon D300

I am a very visual oriented person. Ever since I remember from my childhood, I have been always attracted to images and visual depictions. This is what led to me reading comics. The visual impact. Also, in my house there were always art projects my mother did such as embroidery, paintings among other things. And I was fascinated by colours and drawings. Though I am not very good at drawing, I can certainly appreciate good ones.

Water lily fields submerged near the origin of Mooi river (Taken with Motorola E6). This is one my favourite photos that I have taken.

But coming to photos, some photos make a connection with your very being, inner-self of you. I cannot explain it. But you can experience the photo at some deeper level than the perceptual one. From what I have gathered talking to other people “seeing” the same image, but this experience might be unique, as not every one feels this special connection. You have your favourite photographs, they are really powerful when they speak to you directly transcending the boundaries of space and time.

A poppy flower in a poppy field (Taken with Canon EOS 80D)

I don’t know if there is a cognitive theory that will explain this in terms of our earlier experiences with images or social interactions with media. But this connection that you feel is real and I can’t put it in exact words…

The Peach from Kabul

Kabul in winter

I have visited Kabul in Afghanistan twice. Once in summer (August) and once during winter (February). Mountains and hills are all around Kabul, you cannot miss them from any point in the city. A lot of houses in the city are on the small hills at the periphery and at the centre as I could see.

Kabul street view, note the snow capped mountains in the background

At the time of my visit (c. 2018-19) Afghanistan was Governed by the Ghani government and it was relatively peaceful. There were a lot of apprehensions about our security during our visit to Kabul for about 3 weeks. Not so much about the attacks by the militants, but the kidnappings of foreign nationals for ransom within the city by mafia. I was going alone, the first one to reach there, with one of my colleagues joining me several hours later. We were given a bullet/explosion proof land cruiser for our journey across the city. Each day and each journey was a new route through new neighbourhoods. This way I explored Kabul a little, though through sitting inside a vehicle. All the photos I collected are through our vehicle, resulting in mostly street photography. Thus my experience as a traveller in Kabul was fully “insulated”.

Kabul city scape in summer, note the mountains in the background, compare them with the winter photo when they become snowcapped.

 

The visa was given gratis from the Afghan embassy in Mumbai situated in a bungalow on Walkeshwar Road. Anyways, after an uneventful flight from Delhi, with stunning views of Hindu Kush on the way, I was finally in Kabul. The airport luggage collection was a huge mess, as Kabul airport is not very big. The rush there was immense, but I could get to my bags. I could not get the FRO registration done at the airport as the officer was not there, for which I had to go to another day to an police office in the city (but that is another story).

Kabul city scape in summer

I saw some very humane and amazing murals with messages on the walls. I think they must have been removed by now

Kabul city street mural wall art
Kabul city street mural wall art
Kabul city street mural wall art
Kabul city street mural wall art
Kabul city street mural wall art
Kabul city street mural wall art

As Indians, wherever little we went, there was a genuine warmth and respect shown by the Afghans from all walks of life. They really considered India and Indians as their true friends. Hindi/Urdu was spoken by almost all, an influence of the Bollywood and Indian soap operas. My students knew that (Tulsi Virani was the MHRD Minister of India!). My heart goes out to the teachers who attended our courses, and I hope that they are safe and doing well. It would be great to know how they are doing now…

A snowy experience

The snow in Kabul is a very regular. They told me that it is often used as phrase to say something is very regular “as regular as the snow in Kabul”. Kabul in winter was like a dreamscape. I had never seen snow in person in real life. So this was my first snowfall! It really makes the landscape so beautiful and serene. Some of the scenes, especially of a early morning snow covering everything I recall everytime I think of Kabul. You can see the fort of  Kolola Pushta in the background.

The same view in Summer

Kabul in summer

Though due to our security concerns we could not visit the market areas or restaurants of city per se, we could not visit city at large though I wanted to.  We stayed in a very secure compound in the heart of Kabul in the area of Shahr-e-Naw very close to a fine departmental store Finest Supermarket. I did all my shopping there, though my desire to wander and shop through the bazaars of Kabul remains.

Kabul city street children
Kabul city houses on the hill
Kabul city street children
Kabul city mother and daughter
Kabul city traffic police

 

Something about the food

They say the best way to experience a new culture is to experience their food. I did, but in a limited way. Our personal Afghan cook at did cook us a variety of delicacies for us everyday. Though the bread/naan is always from the neighbourhood bakery called the naanbai. This was a revealation for Ajayji who had read about them but had never seen them. Across Kabul whereever we went there were two shops ever present: a naanbai and a meat shop. Vegetable shops were there but they were not that common, though I saw a few bazaars for vegetables and fruits. Everywhere we went there were roadside stalls selling fruits and dryfruits.

Nanbai in Kabul
Naan bai bakery in Kabul
Naan bai bakery in Kabul

Naan bai bakery in Kabul
Meat shop, butchery in Kabul
Meat shop, butchery in Kabul
A vegetable shop in Kabul

A bucket list item!

On our compound there were several fruit trees including pears, peaches, pomegranates, grape vines and apples . During my summer visit, I could tick off one item from by bucket list. To pluck an apple from an apple tree and eat it. Though it was not fully ripe, the tick off was done!

A garden of fruits
A bucket list item: me picking an apple from an apple tree

Dry fruits

Afghanistan is famously known for its dry fruits. Almonds, raisins, apricots, pistachio, prunes, cherries figs among other things. I got a few of them at the Finest departmental store, though I would have definitely liked to visit the Kabul’s dry fruit markets. Other thing that has been grown, suited to climate of Afghanistan is saffron. I got some Saffron grown in Herat as a gift and I purchased some of it. Saffron is quite cheap as compared to India (~ 500 INR for 5 grams). Again I regret not taking photos of dry fruit stores in the market filled to the ceilings with variety of dry fruits.

Dry fruit seller Kabul city street
Afghan dry fruit seller Kabul
Afghan dry fruit seller Kabul

The other dry fruit worth mentioning, primarily I have not found it anywhere else, is the dried mulberry. The Afghans call it tut, perhaps after shahtut the urdu/persian word for mulberries. The dried mulberry comes in two varieties white and black (the white one being slightly expensive). This has a very different and subtle taste profile, the sweetness the melts in your mouth.

I was gifted the mamra almonds by one of the students from his farm. He came from a Northern province on Tajik border. But otherwise too the almonds are quite cheap. The raisins are in a variety and quality that we don’t get in India. They also have the grapes preserved inside a mud container which creates a unique flavour, though I saw these at Finest but did not puchase them. I came to know about them only later.

The peach of Kabul

Just like the dry fruits, there are lot of options for fresh fruits as well. The road-side stalls as well as early morning transport of fruits to distant parts of the city was testimony to this.

A taxi full of peaches in Kabul city
A lemonade seller in Kabul city street

But the pinnacle of my trip to Kabul which will remain in my memory as long as I live is a peach that I ate there. We had a personal cook for us who would cook our breakfast and dinner in the compound. I like to eat fruits a lot, so on our request he used to keep fruits for us to eat in the pantry. During my summer visit on one of the occasions our cook brought peaches along with usual apples and tangerines. Now this peach was almost size of my fist, the peaches you get in India are almost half the size. And it had a pretty pink-red-orange-yellow colour. When I sniffed it, an absolutely fantastic aroma indicating the fruit was ripe and ready to eat. As I cut the fruit with my trusted Swiss knife of several years, the juices seeped through the cuts in its peach coloured flesh. As I cut close to the seed lodged in the middle, there was a colour change. A deep deep red emanating from the seed spread to the peach coloured flesh of the fruit. These dark colours the peach and the red were an absolute contrast and a sight to behold. It was as if I was looking at a work of art.

As I took the first bite of that fleshy peach, I was thrown total aback. The taste of the peach when it hit my taste buds, it gave me sensations that cannot be described in words. Its almost after five years that I am writing this, but the taste of that peach is still very much with me. The peach exploded flavours in my mouth which I had never experienced in my life. This was along with that sweet aroma that comes from perfectly ripe fruits. My body had a sensory overflow just from that one bite! I almost had an orgasm (foodgasm!?¿) after that first bite! Oooff! That was some taste. I tasted that peach leisurely extracting flavours, tastes and textures. I never knew something could taste that good…

Unfortunately I do not have a photo of the peach, perhaps it belongs to my memories only … Perhaps that is why Babur longed for fruits from Afghanistan when he was in India

We asked the cook to get more peaches like these. He got us peaches the next few days, but they were never as good as the first one. I am not sure given the current situation in Afghanistan that I would be able to visit it anytime soon. But I am still looking for that tasty peach, my senses still searching for that aroma and juices and taste. Perhaps one day, I will be able to go back to Kabul and relish that taste again…

Kabul in winter

 

 

 

What is the concept of basic education?

Introduction

The Government of India are keenly interested in promoting the pattern of Basic education in the country and h ave adopted a number of measures for this purpose. These include programmes of expansion as well . as steps to improve the quality of work ·in Basic schools and their methods and techniques. If this
objective is to be achieved, it is essential that all those who work in the field should have a clear concept of what Basic education means and should be able to distinguish between its essential features and what are mainly matters of detail to b e adjusted in the light of local needs and developing experience.

This Statement about the Concept of Basic Education , which has been prepared by the Basic Education Standing Committee of the Central Advisory Board of Education, is meant to highlight its significant features and. to remove possible misunderstandings. I hope our educationists will ponder over it and try to work out the scheme in the spirit that it envisages, so that Basic education may play its proper role in inculcating the right attitudes and ideals of character and efficiency in our children.
A.K. Azad

 

The Concept Of Basic Education

The term ‘Basic Education’ has been interpreted — and sometimes misinterpreted — in a. variety of ways. This is, to some extent understandable because it is a comparatively recent development and its concept and technique are still in the making. It seems necessary therefore, to state clearly what is meant by
Basic education.

Broadly speaking, it may be stated that the concept of Basic education is the same as defined in the Report of the Basic National Education Committee (the Zakir Husain Committee) and elucidated by the Central Advisory Board of Education. It is clear that the basic principles and techniques, as made out in that Report, should guide and shape educational reconstruction in India.So far as the provision of eight years of compulsory universal schooling and the use of the mother tongue as the medium of instruction are concerned, there is now no difference of opinion about them. They have come to be universally accepted and need no further elucidation, except in so far as it may be necessary to stress the intrinsic wholeness of the entire period of Basic education, covering the Junior as well as Senior Basic grades. The other implications and features of Basic education that need to be clarified and stressed are the following:

  1. Basic education, as conceived and explained by Mahatma Gandhi, is essentially an education for life, and what· is more, an education through life. It aims at creating eventually a social order free from exploitation and violence. That is why productive, creative and socially useful work in which all boys and girls may. participate, irrespective of any distinction of caste or creed or class, is placed at the very centre of Basic education.
  2. The effective teaching of a basic craft, thus, becomes an essential part of education at this stage, as productive work, done under proper conditions, not only makes the acquisition of much related knowledge more concrete and realistic but also adds a powerful contribution to the development of personality and character and instills respect and love for all socially useful work. It is also to be clearly understood that the sale of products of craft work may be expected to contribute towards part of the expenditure on running the school or that the product s will be used by the school children for getting a midday meal or a school uniform or help to provide some of the school furniture and equipment.
  3. As there has been controversy and difference of opinion regarding the position of craft work in Basic schools, it is necessary to state clearly that the fundamental objective of Basic education is nothing less than the development of the child’s total personality which will include productive efficiency as well. In order to ensure that the teaching of the basic craft is efficient and its educative possibilities are fully realised we must insist that the articles made should be of good quality, as good as children at that stage of their development can make them, socially useful and, if necessary, saleable. The acquisition of skills and the love for good craftsmanship have deeper educative significance than merely playing with the tools and raw materials which is usually encouraged in all good activity schools. This productive aspect should in no case be relegated t o the background as has been usually the case so far, because directly as well as indirectly, efficiency in the craft practised undoubtedly contributes to the all-round development of the child; but on the other hand, never should the productive aspect be allowed to take precedence over the educational aspect. It sets up before children high standards of achievement and gives them the right kind of training in useful habits and attitudes like purposeful application, concentration, persistence and thoughtful planning. While it may not be possible to lay down specific targets for productivity at this stage, it should be the teacher’s endeavour to explore its economic possibilities fully with the emphatic stipulation that this does not in any way conflict with the educational aims and objectives already defined. However, it has to be stated that, in the upper classes of Junior Basic schools and in the Senior Basic schools, it should not be difficult for States to lay down certain minimum targets of production in the light of carefully assessed experiences.
  4. In the choice of basic crafts which are to be integrated into school work, we should adopt a liberal approach and make use of such crafts as have significance from the point of view of intellectual content, provide scope for progressive development of knowledge and practical efficiency. The basic craft must be such as will fit into the natural and social environment of the school and hold within it the maximum of educational possibilities. The idea that has been wrongly created in the minds of
    some people that the mere introduction of a craft in a school, e.g., spinning, can make it a Basic school does grave injustice to the concept of Basic education.
  5. In Basic education as, indeed, in any good scheme of education, knowledge must be related to activity, practical experience and observation. To ensure this·, Basic education rightly postulates that the study of the curricular content should be intelligently related to three main centres of correlation viz., craft work, the natural environment and the social environment. The well trained and understanding teacher should be able to integrate most of the knowledge that he wishes to impart to one or the other of these centres of correlation, which form the important and natural foci of interest for the growing child. If, therefore, in-the Junior Basic stage he is not able to do so, it either means that he lacks the necessary ability or that the curriculum has been burdened with items of knowledge which are not really important and significant at that particular stage. It should also be realised, however, that there may be certain items in the syllabus which cannot be easily correlated directly with any of the three above centres. In such cases, which should occur only infrequently, there should be no objection to these being taught according to the methods of teaching adopted in any good school. This means that even in the case of .such lessons, the principle of interest and motivation and the value of expression-work will be utilised. In any case, forced and mechanical ‘associations’ which pass for correlation in many schools should be carefully avoided.
  6. The emphasis on productive work and crafts in Basic schools should not be taken to mean that the study of books can be ignored. The Basic scheme does postulate that the book is not the only or the main avenue to knowledge and culture and that, at this age, properly organised productive work can in many ways contribute more richly both to the acquisition of knowledge and the development of personality. But the value of the book, both as a source of additional systematised knowledge and of pleasure cannot be denied and a good library is as essential in a Basic school as in any other·type of good school.
  7. The Basic scheme envisages a close integration between the schools and the community so as to make education as well as the children more social-minded and cooperative. It endeavours to achieve this, firstly, by organising the school itself as a living and functioning community — with its social and cultural programmes and other activities — secondly, by encouraging students to participate in the life around the school and in organising various types of social service to the local community. Student self-government is another important feature in Basic education which should be envisaged as a continuous programme of training in responsibility and in the democratic way of living. In this way, the Basic school not only helps in cultivating qualities of self-reliance, cooperation and respect for dignity of labour, but also becomes a vital factor in the creation of a dynamic social order.
  8. Basic education should no longer be regarded as meant exclusively for the rural areas. It should be introduced in urban areas as well, both because of its intrinsic suitability and also to remove the impression that it is some inferior kind of education designed only for the village children. For this purpose, necessary modifications may have to be made in the choice of basic crafts for urban schools and even in the syllabus but the general ideals and methods of Basic education should remain the same.

 

from

The Concept of Basic Education, Ministry of Education and Scientific Research Government of India (1957).

I asked ChatGPT to give the Turing Test

Turing Test is a test first conceptualised by Alan Turing, a mathematician and a computer pioneer. Alan Turing made many ground breaking discoveries, in computer science including the architecture of  computing devices which can run any computer programme known after him as Turing Machines. The other type of well known computing device architecture is the von Neumann Machine.

The Turing Test put simply is the ability for a computer programme to have an conversation with a human in a human manner. A programme which can pass a Turing test would mean that it can mimic the human conversation.

The Turing test, originally called the imitation game by Alan Turing in 1950,is a test of a machine’s ability to exhibit intelligent behaviour equivalent to, or indistinguishable from, that of a human. Turing proposed that a human evaluator would judge natural language conversations between a human and a machine designed to generate human-like responses. The evaluator would be aware that one of the two partners in conversation was a machine, and all participants would be separated from one another. The conversation would be limited to a text-only channel, such as a computer keyboard and screen, so the result would not depend on the machine’s ability to render words as speech. If the evaluator could not reliably tell the machine from the human, the machine would be said to have passed the test. The test results would not depend on the machine’s ability to give correct answers to questions, only on how closely its answers resembled those a human would give. (Wikipedia Entry on Turing Test)

 

Now some of the earlier programmes tried to pass the Turing test included chatting programmes such as Joseph Weizenbaum created Eliza  in the mid 1960s. So the Turing tests remained the gold standard for computer programmes to achieve the “human like” thinking. With the latest ChatGPT programme from Open AI Labs, I thought of giving it a try. These are the questions and their responses :

Can you pass the Turing test?

As an AI language model, my primary purpose is to assist and provide useful responses to users based on the input given to me. However, passing the Turing test, which involves convincing a human evaluator that I am a human myself, is not my main goal.

While I am designed to generate human-like responses and engage in natural language conversations, there may be instances where I might not be able to accurately interpret or respond to certain queries. Nonetheless, I will strive to provide the best possible response based on the input given to me.

What questions should I ask in a Turing test?

In a Turing test, the purpose is for the evaluator to determine whether they are interacting with a machine or a human based on the responses they receive. The questions asked should be designed to assess the machine’s ability to engage in natural language conversation, understand the context and nuances of human language, and generate appropriate responses.

Here are some examples of questions that can be asked in a Turing test:

1. What is your favorite book/movie/TV show?
2. Can you tell me a little about yourself?
3. What is your opinion on [a recent news event]?
4. What is the capital city of [a country]?
5. What is the weather like today?
6. Can you recommend a good restaurant in [a city]?
7. What do you think of [a philosophical question]?
8. Can you explain [a complex scientific concept] in simple terms?
9. Have you ever traveled to [a country or city]? If so, what did you like about it?
10. Can you tell me a joke or a funny story?

These questions are designed to test the machine’s ability to engage in natural language conversation, answer questions based on personal experience, provide opinions, and demonstrate knowledge in different areas. However, the specific questions used in a Turing test will depend on the context and purpose of the test.

How would you answer questions listed in the previous chat?

Sure, I can provide sample responses to the questions listed in the previous chat:

  1. What is your favorite book/movie/TV show?
  • As an AI language model, I don’t have the ability to have personal preferences or emotions. However, I can provide recommendations based on popularity or ratings.
  1. Can you tell me a little about yourself?
  • I am ChatGPT, a large language model trained by OpenAI. My primary purpose is to assist and provide useful responses to users based on the input given to me.
  1. What is your opinion on [a recent news event]?
  • I don’t have personal opinions as I am a machine learning model, but I can provide you with information and perspectives on the topic.
  1. What is the capital city of [a country]?
  • The capital city of a country depends on which country you are asking about. Can you specify which country you are referring to?
  1. What is the weather like today?
  • I’m sorry, but as an AI language model, I don’t have access to live weather data. However, I can provide general information on weather conditions in different regions.
  1. Can you recommend a good restaurant in [a city]?
  • Certainly, I can recommend popular or highly rated restaurants in the city you specify. Can you please let me know which city you are interested in?
  1. What do you think of [a philosophical question]?
  • As an AI language model, I don’t have personal beliefs or thoughts. However, I can provide information and different perspectives on philosophical topics.
  1. Can you explain [a complex scientific concept] in simple terms?
  • I can certainly try to explain complex scientific concepts in simpler terms. Please let me know which concept you would like me to explain.
  1. Have you ever traveled to [a country or city]? If so, what did you like about it?
  • As an AI language model, I don’t have the ability to travel. However, I can provide information on different countries and cities, and their attractions or points of interest.
  1. Can you tell me a joke or a funny story?
  • Sure, here’s a joke for you: Why was the math book sad? Because it had too many problems.

How would you rate yourself in the questions that you just now answered?

As an AI language model, I don’t have the ability to rate myself or evaluate my own performance. However, I always strive to provide the best possible responses based on the input given to me, and I am constantly learning and improving through feedback and updates to my training data.

 

As you can see some of the responses are good, while for other its vague and noncommittal. How would you rate the Turing test given by open ai?

Why is it difficult to copy edit your own work?

When I was writing my PhD thesis, as with anyone else it involved multiple drats going back and forth. As far I am concerned writing is never a linear process. At times one cannot even write a single line in a day, and at other times you may finish a couple of sections in a a few hours. Writing is difficult as it involves third level thinking (Dix 2006). You may have several ideas with you, you can also explicate while talking to others. But when it comes to writing it down we find it is not easy. But when we are in the”zone” the writing task becomes a natural thing. Your creative juices flow, the elusive ideas seem to express themselves in words. I usually experience such zone when l am at the end of the world task. The disparate looking ideas are bound together in a coherent whole. The feeling is close to an epiphany of a strange kind. You lose track of time and experience oneness with your work, as of the concrete form of ideas is a physical extension of your self. The feeling can be deeply satisfying to see your ideas on a concrete form. Mihaly Csikszentmihalyi uses the term “flow” to describe such an experience.

I experience the similar thing while reading a book. There are times when even reading a couple of sentences feels like a chore. While at other times when I am in the flow a hundred pages are finished in a couple of hours. The result send effortless. Words just seen to read themselves or to you. Of course it also depends on the kind of book one is reading. Technical books will take a longer to read.

When you are reading easily, you actually don’t read the entire words, letter by letter. Rather there is some sort of guess work or pre-processing that happens. Typically by looking at the starting letter and the end letter and also estimating the size of the word, we can actually guess the word before we can read it correctly. That is our cognitive system can fill in the gaps when we are dealing with familiar information. This makes the reading fast for experienced learners. A full use is made is of the repertoire of words that we know, and also rules of grammar. We expect certain words to follow certain words. And at times our system will fill in the gaps by itself when it finds some. This way the reading becomes effortless and we can make name out of it easily. Such fast refund comes with experience and knowing the language. When your children have difficulty in reading they have both problems. Their prediction system is not strong so they have to read each word and each letter in the word individually and only then they are angle to make sense. This then boils to be able to recognise the symbols as quickly as possible.

But how do we recognise the symbols that we see? There are several theories that attempt to explain our recognition of the symbols. The template theory posits that there are as many templates in our long term memory as many symbols we can detect. But this assumption of the theory puts severe demand on the long term memory and also on the processes which would the pattern recognition. A simple example which puts the template theory into spot is that we can recognise a letter in its various forms. The sheer number of fonts and handwriting, some of it bordering on illegible, we can recognise with little efforts lots severe strain on the template theory. The fact that we can also recognise the shape of fonts we have never seen before also poses a challenge.

The feature theory on the other hand posits that the long term memory has a set of features of the symbols which are essential in the symbol. For example, to recognise letter “w”, the feature set might include two lines slanting to the left and two lines slanting to right such as \ / \ /. This as soon as our sensory register gets this input of such lines we immediately pre process such input to a “w”. The feature theory posits three steps in pattern recognition which are collectively called as Analysis-by-Synthesis. In this process the pattern is broken down into its features, then these features are matched with LTM and finally a decision about the pattern is taken. Thus with this theory we require much less number of items in our long term memory. The analysis-by-synthesis is completely driven by the data that impinges on the sensory organs. 

Some of the challenges that this theory faces include ambiguity of how we deal with ambiguity in recognition of the patterns especially when the data is similar. In particular it does not answer our ability to consider importance of context in which the patterns appear and the sensory data itself is not good enough discriminator. In many cases turns out that we rely on other knowledge and information also to make sense of the patterns, in which case the feature theory alone cannot provide good explanations. For example, consider the Greek letter $\Delta$. Though we can identify it as such, the meaning it conveys can be heavily dependent on the context. We take three such examples.

  • If it is seen in a sentence in Greek it will be interpreted as a sound “de” Το Δελχί είναι η πρωτεύουσα της Ινδίας (Delhi is India’s capital.).
  • Now if the same letter $\Delta$ is seen in a mathematical context such as $\Delta ABC \cong \Delta PQR$, it represents a triangle and the sentence is read as “Triangle ABC is congruent to triangle PQR”.
  • Finally, if the symbol $\Delta$ appears in a physics formula, lets say $\Delta E = E_{2} – E_{1}$, it represents a difference in the two values of $E$.

Or consider the two sentences below

In the first sentence we will probably read it as “The number of participants was 190 (one hundred and ninety)” while in the second sentence we would read it as “I go there often”. Note here that the visual pattern is the same in both the sentences. Yet the context of the sentence makes all the difference in how we interpret the pattern. From such experiences we must conclude that context affects the pattern recognition by activating some conceptual information from LTM or pre-synthesising the pattern. Thus our cognitive system adds more information based on the contexts to the perceptual data to make sense of the patterns and context establishes what to expect in the incoming patterns. 

Now this adaptive feature of the our cognitive system can be very useful and allows us to be much faster than just being dependent on the perceptual information. But at times it can be maladaptive also. This notion brings us back to the title of this post. As I completed my first draft of the thesis, and gave it for comments, I discovered to my extreme horror and embarrassment that it was full of elementary grammatical mistakes. In the flow of writing down my ideas, I chose to just go with them. Though I did review what I had written, I did not find any obvious faults in it. This is something that you might have also experienced. It is difficult to see “obvious” break in ideas or abrupt endings in your own writing, and this of course also includes “trivial” grammar rules of punctuation and articles as such.  But when you are proof-reading work of someone else both “obvious” and  “trivial” errors are markedly visible. I can say this as I have copy-edited and proof-read several long and short works, where I did found out the very same errors in other works which I could not in my own work. Thankfully, in my thesis most of the issues were of “trivial” grammar and no “obvious” conceptual or fundamental issues were pointed. I then furiously began correcting the “trivial” grammar issues in my work. 

 

Why is this so? Seen in the framework of analysis-by-synthesis model, we know what we have written or wanted to write and our pre-synthesising cognitive system fills in the obvious gaps and creates the required and expected patterns contextually where they are found missing. We tend to “skip” over our writing as we read it in a flow, with background and context of why the text was written and what it wants to say. All the “obvious” and  “trivial” errors and gaps are ironed out with the additional contextual information that we have about our own work. So we have to be extra-careful while proof-reading our own work. When we are reading work written by someone else, all this background information is not available to us, hence pre-synthesising of patterns happens at a lower level. This leads us to find “obvious” and  “trivial” errors and gaps much easily.

I found out that though I can do a good job of proof-reading other persons work on a computer (using the record changes/comments on a word processor) , for proof-reading my own work I usually take a printout and work on it with a pen. The concrete form of my work perhaps helps me in minimising the pre-synthesising that happens.  I usually take red ink for proof-reading, perhaps reminiscing of how teachers in schools grade assignments. 

 

References

Chapter 2 Hunt, R. R., & Ellis, H. C. (1999). Fundamentals of cognitive psychology. McGraw-Hill.

A. Dix (2006). writing as third order experience Interfaces, 68, pp. 19-20. Autumn 2006.

 

Goat’s beard or the hunt for the elusive and mystic flower

In one of my evening walks along the Mooi river front near my house I noticed an unusually large dandelion like spherical seed pod. By unusually large I mean size of a tennis ball!

The red/purple marks on my fingers are due to mulberries growing on the river bank that I had picked and eaten just a while back.

The usual spherical formations that I had seen so far were of the size of a centimeter or two in diameter, so this one was a huge one. The dandelion like seeds (pappus) are usually very delicate and have very fine structure. In contrast to the dandelion, these seeds were huge (scaled by at least 10 times or more), and even the construction seemed very robust. Instead of single hair like structures as in the normal dandelion, it had a net type of structure.

A typical dandelion. Where are the other half seeds gone to?

The giant dandelion!

So I thought inductively, that whatever by this flower is it should have a proportionally bigger display. So in the coming days I like a professional stalker tried to “stalk” this flower. But this was something that did not succeed. It is perhaps to do with already knowing what you are looking for. I was not “seeing”, I was just “looking”.In philosophy of science there is a concept called theory ladenness of data. What this essentially means that there are no “pure” observations. We always need some background knowledge to make sense of these observations. The conceptv of pure observations was one of the conceptual backbones of the logical positivist approach to philosophy of science. They claimed that just pure observations can be done and can be used as a criteria for adjudging the correctness of theories. But several schools of thought conclusively showed that such pure observations are not possible. We always have a theoretical framework in which observations are done, with several declared and undeclared assumptions accepted as a part of that framework.In my case I didn’t know what the flower looked like. I knew what other dandelions looked like, so I was constructing my model of the flower on those designs. I had deliberately tried to avoid using the internet for the search. I mean I knew where the plant was so it would be trivial to find its flowers. But even for a couple of weeks of almost daily looking I would only find the tennis ball sized globes of seeds but not the flowers themselves. There was the proverbial smoke but I couldn’t see the fire.Now the thing was I was visiting this stretch of wilderness during the evenings. And then after two weeks of futile attempts to find the flower it stuck me that this might be a morning flower. So by the time I went in the evening the flower had done is business and had signed off. So this would be unlike other dandelions whose flowers persist for days and are operationally on through the day. So I decided to test this hypothesis the next morning. And voila there it was. I was expecting a grand flower which would do justice to the grand seed ball it created. But the flower was a damp squib. It was not at all grand to look at. I mean of course it was beautiful, but I was expecting a bigger flower.

Now armed with the knowledge about how the flower looked, I was able to trace the flower from a couple of wild flower guides. The plant was Tragopogon pratensis. The plant is also known as goat’s beard and is but a native of Southern Africa. Thus concluded the mystery of the great ball of flying seeds. In the process I discovered a whole bunch of morning flowers which I did not know as I usually visited only during the evenings.

All images CC by SAhttps://en.wikipedia.org/wiki/Asteraceae