10 July 2026

Each season chases out the former

 

Each season chases out the former,

All seasons lie in wait in the Sky,

For the extant to be chased away:

Spring lies in wait 

For Winter to be chased away,

As Summer waits for Spring

To be chased away,

Then Autumn, then Winter,

They are all hiding in the Sky.


One day a season or more will get tired,

Someday a season or more will slow down,

And thus fall far behind,

And, forever lay hidden in the Sky.

Will it be Winter, will it be Spring?

Will it be Autumn, will it be Summer?

Only the Sky can tell: 

For It only downs the Veil,

It also holds the Rotating Wheel.


Love will only grow

 


Won't not look back
Before I go,
If I look back,
Won't be able to go,
The pain will only show,
My love will only grow. 



05 July 2026

Tetration of the imaginary number 'i'

 


I received this Sunday gyan today:

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The knowledge- Sunday Reading

Studies suggest that walking in a park or near a water body reduces cortisol (stress hormone) by 30%.

Crazy fact: In just 1 hour, more solar energy hits Earth than humanity uses in a whole year. And in <8 hours, enough sunlight hits Earth to power us for a year. 

i^i = 0.20787957635….. Imaginary number to the power of imaginary number is a real number be-cause of Euler's formula, which connects trigonometric functions with complex exponential func-tions.

...and more reading

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The third factoid was pretty interesting. I asked help of AI to find how i^i = 0.20787957... I added a bit of my own complexity just for fun. I asked AI thus: What would be i to the power of i? I saw somewhere that it would be 0.207.... This is amazing , is it not? A decimal fraction? What would be tetration of i , say 4 subscript i? 

Now, tetration is an maths animal I had just heard about. Tetration of any number would be that number to the power of that number, to the power of that number, to the power of that number...and so on. In the case of 4 subscript i(or, ⁴i), it would be i to the power i, to the power of i, to the power of i, to the power of i, or in other words: i^(i^(i^i)), or,


Claude AI replied thus:

Yes, i^i is one of the loveliest surprises in complex analysis — a pure imaginary number raised to a pure imaginary power ends up being a real number.

Why i^i is real

Using Euler's formula, i = e^(iπ/2) (writing i in exponential form). So:

i^i =(e^(i*π/2))^i = e^(i*i*π/2) = e^(-π/2)

And e^(−π/2) ≈ 0.2078795...

It's a real number, but it's not a fraction in the sense of a ratio of integers — it's irrational (in fact, transcendental). 0.207... is just its decimal approximation, not a terminating or repeating fraction.

Now the tetration: ⁴i = i^i^i^i

Tetration stacks exponents from the top down: ⁴i = i^(i^(i^i)). Let's build it one level at a time, always using the principal branch:

Level 1: a₁ = i

Level 2: a₂ = i^i = e^(−π/2) ≈ 0.20788 (real, as above)

Level 3: a₃ = i^(a₂). Since a₂ is real, this is:

i^(0.20788) = e^(0.20788 * i*π/2) = cos(0.3266) + i*sin(0.3266) =approx 0.9472 + 0.3208i

Level 4: a₄ = i^(a₃), now with a complex exponent:

i^(a₃) = e^((a₃)*i*π/2))

Working through the complex arithmetic (multiplying a₃ by iπ/2, then exponentiating) gives:

⁴i= approx 0.0502 + 0.602i

Its magnitude is about 0.604, and it sits at an angle of roughly 85° from the positive real axis.

A fun fact: as you keep stacking more i's (⁵i, ⁶i, ...), the tower actually converges to a fixed complex number rather than blowing up or oscillating forever — infinite tetration of i converges to approximately 0.4383 + 0.3606i. That's a much rarer property; most bases don't have convergent infinite towers.

Explaining e^(−π/2): That line comes from calculating i^i.

Here's the reasoning behind it:

Step 1: Write i in exponential form.

Any complex number can be written as e^(iθ), where θ is the angle it makes on the complex plane. The number i sits at 90° (π/2 radians) on the unit circle, so:

i = e^(i*π/2)

Step 2: Raise it to the power i.

i^i = (e^(i*π/2))^i

When you raise a power to a power, exponents multiply:

= e^(i*π/2*i) = e^(-π/2)

since i² = −1. Notice the i's cancel out — that's the key step. What started as an imaginary exponent multiplying another factor of i becomes real, because i times i is just −1.

Step 3: Evaluate the number.

π/2 ≈ 1.5708, so we need e^(−1.5708). Since e ≈ 2.71828, this is 1 divided by e^1.5708, which works out to:

e^(-π/2), approx 0.2078795...

Why this feels surprising: you'd expect an imaginary number raised to an imaginary power to give you something imaginary or at least complex. Instead, the two imaginary-ness factors cancel each other through i² = −1, leaving a plain real decimal — and an irrational one at that, not a fraction, just a number that happens to start 0.207.../2) ≈ 0.2078795...further:

Me:

The fun fact, ' as you keep stacking more i's (⁵i, ⁶i, ...), the tower actually converges to a fixed complex number rather than blowing up or oscillating forever — infinite tetration of i converges to approximately 0.4383 + 0.3606i. That's a much rarer property; most bases don't have convergent infinite towers.' has got me intrigued. Have we found another e-like number as we tend tetration of i towards infinity, albeit in the complex plane?

Claude AI:

Not quite an analogue of e, but let's look at what makes e special versus what makes this fixed point special — the comparison is illuminating.

What actually makes e "e-like"

e is fundamental because it shows up as the unique solution to many independent, unrelated problems: the base where d/dx(eˣ) = eˣ, the limit of (1+1/n)ⁿ, the sum of 1/n!, and so on. It's a universal constant that keeps appearing across completely different branches of math — that ubiquity is what earns it the special status.

What the fixed point 0.4383 + 0.3606i actually is just the solution to one specific equation:

z = i^z

That's it. It's the fixed point of this particular map (raise i to the power of the input, repeat). It's a legitimate and interesting number — but it's not showing up independently all over mathematics the way e does. It's more like asking what does the sequence x, cos(x), cos(cos(x)), ... converge to? (answer: the Dottie number, ≈0.739085, the fixed point of cos(x) = x). That's a genuinely analogous situation — a real fixed point of a specific iterated function, interesting in its own right, but not a universal constant.

Where the real analogy lies

If you want the actual "complex-plane e," you don't need to look for a new number at all — e itself already lives on the complex plane and does the heavy lifting there via Euler's formula, e^(iθ) = cos θ + i sin θ. That's the bridge between e and complex numbers, and it's precisely the tool we used to compute i^i in the first place.

What you have found, though, is something worth appreciating on its own terms: a genuine example of a complex fixed point of an iterated exponential map. Your complex fixed point is the counterpart of that convergence question, just off the real axis. So: a nice number, a legitimate mathematical object, but its significance comes from being a fixed point of this one map — not from popping up everywhere the way e does.

Me:

Can this be geometrically created? Will this point be same point in space wherever we are on earth?

AI Claude:

Good questions — they touch two different ideas, so let's separate them.

Same point wherever we are on Earth?

Yes — but the reason is simpler than it might seem: this point isn't a location in physical space at all. It's a point in the complex plane, which is a purely mathematical construct — a 2D coordinate system where one axis represents real numbers and the other represents multiples of i. It has nothing to do with geography, gravity, or your position on the planet.

So 0.4383 + 0.3606i is the same abstract mathematical object whether you compute it in Bengaluru, Antarctica, or on the Moon — the same way "7" or "π" doesn't change depending on where you are. It's a number, not a place.

Can it be geometrically constructed?

Here there are two very different meanings of construct, and the answer differs for each:

1. Classical straightedge-and-compass construction — almost certainly no.

Classical constructibility (the kind used for bisecting angles or constructing regular polygons) only works for a specific class of algebraic numbers — ones reachable by a finite sequence of square roots. Our fixed point comes from solving z = i^z, a transcendental equation with no closed algebraic form. Numbers like this are expected to be transcendental (not the root of any polynomial with rational coefficients), which puts them firmly outside what compass and straightedge can ever reach — much like you can't classically square a circle because π is transcendental.

2. Iterative geometric construction — yes, and it's genuinely elegant.

You can construct it as a limiting picture through repeated geometric steps:

- Start at any point in the complex plane

- Apply the transformation z → i^z (a rotation by angle proportional to Re(z), combined with a scaling by a factor depending on Im(z))

- Plot the new point

- Repeat

If you connect the successive points, you get a spiral that winds tighter and tighter, converging visually toward 0.4383 + 0.3606i. This is the complex-plane version of a cobweb diagram, the same visualization technique used to show the real Dottie number (fixed point of cos x) spiraling into place. It never exactly arrives in finitely many steps — but it approaches arbitrarily closely, which is a legitimate and beautiful way to construct it geometrically, even though it's not the classical Euclidean sense of the word.

Want me to actually plot that spiral for you? It would visually be a satisfying way to see this whole conversation come together.

Me:

Yes please.

AI Claude:

Here it is:




03 July 2026

Fill my night with love

 


Call me as a lighthouse
To a ship adrift yonder,
Fill my night with light,
Fill my night with love.




01 July 2026

A creeper's 'leap of faith'


This is a creeper growing across the road that runs in front our building. The 'crossing' is a little away from our building. Don't know how two creepers from two ends got entwined with each other, yet kept themselves high above the road. Could be human intervention, but unlikely because who would stand up in the middle of the road and tie the creeper(s) together?  And to what avail?


When I posted this image on a social media platform with the note that I have written above the image, my friend 'R' replied with this explanation which he had acquired from some sources:

The Touch Trigger: As a vine sweeps through the air (a process called circumnutation), it senses physical contact. The tendril's touch sensors are highly sensitive, capable of registering weights as light as a fraction of a gram.

Differential Growth: Upon contact, cells on the side touching the support contract, while cells on the opposite side rapidly elongate. This uneven growth quickly forces the tendril to curl tightly, securing a grip

Me: 

Dear R: Thanks for the riposte.

However, this only gives the process. The motivation of the creepers to join hands (so to speak) is not given. Can it be likened with cross pollination, where both parties benefit. Or, is it parasitic approach of one against another? Or, is it something inexplicable in the language that we know. In fact, when I see this phenomena and I read along with tree bridges of Meghalaya, there are many unanswered questions.

R:

It is a very interesting mode of survival and propagation.. tendrils have a very sensitive surface design.. the plant kingdom is best studied in rain forests .. including the complex root system … fires destroy them completely and in a year or so they are back .. its a science that needs to be studied if it interests you!

Me:

It does interest me. What piques my interest is how do the tendrils work against gravity? Unlike the tree bridges of Meghalaya, where there was human intervention of generations to get the bridge going, here the tendrils are seemingly spanning the gap of 50 feet, at a height of about 20 feet(all buses and trucks, even 18 wheeled ones, pass under this tendril embrace) without any assist. This embrace is no more than 5 years old.

At this point I took help of gyani AI Claude:

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Claude:

What a fascinating observation and conversation! Let me engage with the questions you and R have been discussing.

What you're seeing in the photo: The image shows two creepers/vines that have grown from opposite sides of the road and met in the middle, their tendrils intertwined at considerable height — with enough clearance for large vehicles to pass beneath. That's a remarkable natural achievement.

On your core question — how do tendrils work against gravity?

This is actually the most intriguing part. A few mechanisms are likely at play:

- Thigmotropism + circumnutation (as R's screenshot explains): as the vine sweeps through the air, it keeps extending outward. The tendril doesn't "fight" gravity so much as it grows faster than gravity can pull it down — especially in humid, warm climates like Bengaluru's.

- Tensegrity: once two tendrils touch and grip each other (using exactly the touch-trigger and differential growth mechanism described in R's screenshot), they create a mutually reinforcing tension structure — each holds the other up. This is actually structurally elegant: the embrace distributes load between both plants.

- The 50-foot span without assist: this strongly suggests the vines used intermediate supports — perhaps an overhead wire, a branch tip, or even a passing vehicle briefly — at some point. A single chance contact in the right spot could have initiated the whole bridge.

On your deeper question — motivation: mutualistic, parasitic, or something else?

This is where it gets philosophically rich. Most botanists would say there's no motivation in the intentional sense, but functionally:

- It's likely mutualistic — each vine gains a structural anchor from the other, potentially extending both their reach toward light.

- It's not classically parasitic since neither appears to be drawing nutrients from the other (unless one is a hemiparasite like a mistletoe-type).

- Your instinct to compare it to the Meghalaya living root bridges is very apt — the difference being time scale and agency: those bridges took human guidance over generations; this happened in ~5 years, spontaneously.

The unanswered part:

What remains genuinely mysterious is the initiating moment — how the first contact across that 50-foot gap was made. Wind, a passing tall vehicle brushing a tendril sideways, or sheer extended growth are possibilities. But you're right that it deserves a blog post — and perhaps a closer look at what species these are, which might reveal more about their growth strategy.

Me:

I sought clarification from Claude regarding 'as it grows faster than gravity can pull it down' thus:

What does this (as it grows faster than gravity can pull it down) actually mean? Does it mean that the acceleration of the tendrils towards the sky is more the retardation caused by the acceleration due to gravity?

Claude:

That's a sharp catch — and honestly, my earlier phrasing was sloppy. Let me correct it properly.

No, it doesn't mean that, and the statement is physically problematic as written. A tendril is not a projectile. It isn't moving upward with any velocity or acceleration that could "outpace" gravitational pull. Gravity acts on its mass continuously, and nothing in plant growth generates an upward force that counters gravitational acceleration in that Newtonian sense.

What I should have said is this:

The tendril grows incrementally, cell by cell, at its tip. Each new increment of growth is essentially supported by the rigid structure behind it — the already-hardened older portion of the vine. So the question isn't "how does the tendril overcome gravity?" but rather "how does the structure behind the growing tip stay rigid enough to act as a cantilever?"

The honest answer is: it largely can't, over 50 feet, without intermediate support. A pure unsupported cantilever of that length from a soft vine is biomechanically implausible.

What this means for your observation:

The more physically coherent explanation is that the vines found opportunistic intermediate contacts along the way — a branch tip, an overhead wire, anything — even momentarily, that allowed the tendril to hook on and extend further. The final "embrace" in the middle may be the last and most visible link in a chain of smaller, less obvious contacts. So your instinct to call it inexplicable isn't wrong — the initiating geometry of how that first mid-air contact was made across the full gap remains the genuinely open question.

Me:

Thanks. I will try to upload a zoomed picture of the vine(s). Perhaps, you will be able to identify the vines and the cause for each to seek the other. I will come back to you once I have a picture with  a higher resolution.

Claude:

That sounds great! A clearer, zoomed-in photo would help a lot — ideally one that shows:

- The leaf shape and arrangement (alternate, opposite, compound?)

- The tendril structure (do they arise from leaf axils, stem nodes, or modified leaves?)

- The stem cross-section if visible (round, square, winged?)

- The point of contact/embrace between the two vines

With those details visible, identifying the species becomes much more feasible — and the species identity could genuinely shed light on your "motivation" question, since some vines are known to exhibit particular growth strategies (light-seeking, support-seeking, etc.) that might explain why these two reached toward each other.

Looking forward to seeing the photo when you have it!

Me:

Photos from same side of the road, focussed on other side of the road, and from below the embrace. Unfortunately, I noticed that the creeper is withering on the vine at the far side.






Claude:

These new photos are much more revealing! Let me work through what I can now see.

The vine identity: The heart-shaped (cordate) leaves visible clearly in Images 2 and 3 are quite distinctive. This looks very likely to be Ipomoea species — possibly Ipomoea cairica (Mile-a-Minute vine) or Ipomoea indica, both extremely common in Bengaluru, vigorous climbers, and known to colonise walls, trees, and overhead structures rapidly. The leaf shape, size, and the way the stems trail and dangle are all consistent with this identification. The thin, wiry bare tendrils/stems visible hanging down in Image 3 also match Ipomoea's growth habit.

The crucial structural revelation: Image 3 is the most important photograph you've taken. Look at the upper left — the vine is clearly growing along and over the compound wall, and has then extended outward and upward. More significantly, you can see utility/telephone wires crossing the road at that height. The vine almost certainly used those wires as its intermediate support — not a dramatic mid-air leap, but a patient, opportunistic colonisation of an existing wire infrastructure. This resolves the biomechanical puzzle we discussed earlier.

The withering you noticed: This is concerning and botanically significant. Ipomoea, despite its vigour, is sensitive to being cut at the root. If the wall-side plant has been trimmed or its root disturbed, the extended portion dies back from the far end first — exactly what you're observing. It may also simply be the older, less-leafed portion showing seasonal dieback while the root-side remains green.

On your original question of "motivation": Ipomoea is a pure light-seeker — its entire growth strategy is to find the maximum sun exposure. The road gap, being open sky, would have been an irresistible phototropic pull. There is no mutualism or parasitism between the two vines — both were independently following the same imperative: grow toward light. The "embrace" was incidental geometry, not intent.

Me:

I think your assumption regarding wires being present in and around the creeper is incorrect. The cables that are seen are way beyond the crossing place of the creeper.  In any case there are no cables running on the left side of the road as can be seen clearly from the 3rd picture. The second picture gives us the leap of faith, literally. It is shot from below the crossing point. You may want to change/adjust your findings accordingly.

Claude:

You are absolutely right, and I apologise for that hasty inference. Looking at Image 3 again carefully — the cables visible are on the right side of the road, well beyond the crossing point, and there are clearly no cables on the left wall side from which the vine originates. Image 2, shot from directly below the crossing point, confirms this: it is an open-sky gap with no wire infrastructure anywhere near the embrace.

So the biomechanical puzzle is fully reinstated, and is in fact deeper than before.

What Image 2 actually shows

Looking at it carefully from below — the vine has made a genuine unsupported crossing. The stems are laden with leaves all the way across, which means this is not a wispy trailing end but a load-bearing, self-supporting arc. The leaf density itself adds considerable weight, making the achievement more, not less, remarkable.

A revised structural hypothesis:

The only physically coherent explanation now is that the vine grew along the top of the compound wall first, building its anchored mass there, and then sent out exploratory shoots over the road. These shoots, being young and very light at their growing tips, could extend surprisingly far if the wind was consistently blowing from the wall side toward the tree side — essentially being carried incrementally until a tendril tip made contact with a branch of the tree on the opposite side. Once that first contact was made and gripped, subsequent growth consolidated the bridge.

This makes wind the unsung protagonist of your story — not wires, not human intervention.

The withering observation becomes more significant now — if the far-side tree's branch that anchors the vine is dying or was trimmed, the entire unsupported arc could eventually collapse. It would be worth photographing the anchor point on the tree side if possible.

Me:

I will try to take a picture of the anchoring point.

Later...

Me:

It was not possible to get a picture of the anchor (as you call it) as it was at the other side of the wall. And, the wall completely blocked the view inside of the walled area. However, I found no tree growing higher than the height of the wall, nor any electric pole, just behind the wall. But what can be seen from the third picture, is the thick and verdant growth of the creeper along the wall. At some places, as the creeper went along the wall, offshoots went down towards the pavement below. This can also be seen in the third picture. Perhaps, the wall itself is the 'anchor' of the creeper as it throws itself across the road?

Claude:

This is a brilliant observation, and I think you have cracked it: The wall as anchor — not just support, but launch platform

Look at Image 3 again with fresh eyes. The vine has colonised the entire top of the wall, building up over time a thick, dense, almost continuous mat of growth. This mat is not just resting on the wall — it is gripping it, rooting into its surface, interweaving with itself. The wall has essentially become a living structure, with the vine as its skin.

This changes everything structurally. The vine is not launching from a single point like an arrow. It is launching from a distributed base — a long, anchored, load-sharing platform of its own making. The offshoots you observed going down toward the pavement are also significant: they tell you the vine has so much vigour and mass on the wall that it is sending explorers in every direction — downward, outward, and across.

The crossing then becomes almost inevitable

Once the wall-mat reached the corner or the point closest to the road gap, the vine's natural phototropic drive would send shoots outward into the open sky above the road — the brightest available space. With the entire wall-mat acting as a collective anchor, even a relatively thin shoot extending across could be supported, the way a fishing rod can extend far beyond its handle because the handle is firmly gripped.

What the offshoots going downward tell us:

This is actually the most elegant detail you have noticed. It confirms that the vine is not under any directional compulsion — it is not "trying" to cross the road. It is simply growing in all available directions simultaneously. The crossing is the one that succeeded spectacularly and became visible. The downward offshoots are the forgotten siblings of that same exploratory impulse.

Your instinct is exactly right — the wall is the anchor, the protagonist, and the launch pad all in one. The road crossing is its most dramatic expression.

Me:

I think the loop is not complete. The jury is still out on the motivation of the creeper's leap. Is it growth? Is it try to chart uncharted waters? Is it 'emergence'?

Claude:

You are absolutely right — I was too hasty in declaring the story complete. The how has a reasonable answer now. The why remains genuinely open. Let me lay out the three possibilities you've named honestly:

Is it simply growth?

The reductionist answer. The vine grows because it grows — phototropism, thigmotropism, cell division. No more "motivation" than a river has motivation to flow downhill. This answer is scientifically defensible but feels insufficient, precisely because it explains the mechanism while saying nothing about the outcome — a 50-foot aerial crossing that has persisted for years.

Is it exploration — charting uncharted waters?

This is more interesting. Some botanists and plant behaviour researchers — Stefano Mancuso being the most prominent — have argued seriously that plants make something analogous to decisions, allocating resources toward promising directions and withdrawing from dead ends. The downward offshoots you noticed that found no support and withered — versus the aerial crossing that succeeded and consolidated — could be read as exactly this kind of exploratory trial-and-error. Not conscious, but not purely mechanical either.

Is it emergence?

This may be the deepest framing. The crossing was not planned by any single tendril or any single growth decision. It arose from the accumulation of thousands of small, local, uninstructed growth events — the wall colonisation, the mat formation, the simultaneous multi-directional exploration — producing a global outcome that no single part "intended." That is emergence in its precise meaning.


The jury is indeed still out. And perhaps that is exactly where your blog post should leave it too — not with a tidy answer, but with the question itself held open, respectfully.


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24 June 2026

The percentile conundrum

 

There is no such thing as 100 percentile. The definition of a percentile is:

The value below which a given percentage of observations fall.

For the 100th percentile, it would mean:100% of observations fall below this value. But that is not achievable. The maximum value in a dataset cannot have 100% of values below it, because it itself is in the dataset. So strictly speaking, no value can be at the 100th percentile. So what is the maximum value?

The maximum score is technically at the 99th percentile, or 99 plus as many decimals as the total set increases in size (or more precisely, approaches but never reaches the 100th). It simply means:

Scored higher than 99%(or 99.9%, or 99.99%, or, 99.999%...) of everyone else. That is the ceiling, not because the score is 99, but because the ranking system tops out at 99, or more correctly, anywhere between 99 and 100, 99 inclusive.

So, when I saw this report in Republic TV, I was a little confused. 


Asked help from Claude AI to clarify. I asked:

If the number count of the set taking test approaches infinity, will the first person's percentile approach 100? For example, this Republic TV report says one test taker scored 100 percentile in 4 subjects. Is this possible?

Claude:

Part 1: Does percentile approach 100 as N approaches infinity?

Yes, mathematically:

> Percentile of Rank 1 = ((N − 1) / N) × 100

N (total candidates) : Rank 1 percentile

10      : 90.00

100      : 99.00 

1,000      : 99.90

11,00,000 (11 lakhs) : 99.9999% 

| ∞ | approaches 100, never reaches it

So it is an asymptote — forever approaching 100, mathematically never arriving.

Part 2: Is the Republic TV claim valid?

Almost certainly not mathematically precise — but here is what is likely happening. The rounding explanation

With 11 lakh (1.1 million) candidates, Rank 1's actual percentile is:

> ((11,00,000 − 1) / 11,00,000) × 100 = 99.9999%

When rounded to two decimal places → 100.00

So CUET likely rounds to two decimal places, and 99.9999% rounds up to 100.00 — which they then report as "100 percentile."

The Republic TV report is a rounding artifact, not a mathematical truth. With 11 lakh candidates, the top scorer's percentile is so close to 100 that after rounding it displays as 100 — but the strict answer from our earlier discussion still holds: 100th percentile is unreachable in principle. CUET is essentially trading precision for readability.

Me:

Thank you.  So the second and third positions would also get 100 percentile with rounding off? Republic TV reports, 'The high level of competition was evident in the results, with Saksham Goyal securing second place with 1230.82 marks, narrowly followed by Himachal Pradesh’s Udit Chaturvedi in third with 1207.21 marks.'

Claude:

Calculations

> Percentile = ((N − rank) / N) × 100

| Rank | Calculation | Actual Percentile | Rounded to 2 decimal places |

|1 (Devina)| (1099999 / 11,00,000) × 100 | 99.999909% | 100.00% |

|2(Saksham)| (1099998 / 11,00,000) × 100 | 99.999818% | 100.00% |

|3 (Udit)| (1099997 / 11,00,000) × 100 | 99.999727% | 100.00% |

So yes — all three round to 100.00%

With 11 lakh candidates, each rank step changes the percentile by only:

> 1 / 11,00,000 × 100 = 0.000091%

That difference is so tiny it is completely invisible after rounding to 2 decimal places.Yes, with a population as large as 11 lakhs, rounding to 2 decimal places causes the top several ranks to all display as 100 percentile — even when their actual scores differ meaningfully. Percentile is a blunt instrument at the extremes.

Complete picture

|Rank| Name |Marks|Actual Percentile|Rounded Percentile|

| 1 | Devina | 1232.19 | 99.999909% | 100.00% |

| 2 | Saksham Goyal | 1230.82 | 99.999818% | 100.00% |

| 3 | Udit Chaturvedi | 1207.21 | 99.999727% | 100.00% |

Score gaps

| Comparison | Marks difference |

| Rank 1 vs Rank 2 | 1.37 marks |

| Rank 2 vs Rank 3 | 23.61 marks |

| Rank 1 vs Rank 3 | 24.98 marks |

Two interesting observations

1. The reporter called Rank 3 "narrowly behind" Rank 2 — but the gap between them (23.61 marks) is 17 times larger than the gap between Ranks 1 and 2 (1.37 marks). If anything, Ranks 1 and 2 are the narrow contest, not 2 and 3.

2. All three show 100.00% percentile — yet their raw scores tell a far more differentiated story, with nearly 25 marks separating first from third.

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Belgium holds Iran to 0-0 draw

 

Received this tongue in cheek today:



I can foresee that Iran will change her name from 'I ran' to 'I stay'.



 

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