Tax deduction under 80G under the new tax regime with special reference to the recent Assam floods

 Here is a discussion with Chatgpt on Tax deduction under 80G under the new tax regime with special reference to the recent Assam floods:

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Me:

Under the new Income tax regime, are contributions to Chief Minister's Relief Fund and Religious Institutions under 80G exempt from Income tax ? 

(If anyone wants to contribute to Chief Minister's Relief Fund Assam, s/he can do here.

https://cm.assam.gov.in/donate )

Chatgpt:

No. If you opt for the new income tax regime (Section 115BAC), you generally cannot claim a deduction under Section 80G for donations. This applies regardless of whether the donation is to a Chief Minister's Relief Fund or to an eligible charitable institution. 

A note about religious institutions

There is often confusion here.

Donations to approved charitable trusts or institutions that have a valid 80G registration may qualify under the old regime, even if the institution has a religious association, provided it satisfies the conditions laid down in Section 80G. 

However, donations made purely for religious purposes (for example, offerings, pujas, hundi donations, or donations to institutions that do not qualify under Section 80G) do not qualify for deduction.

If you are under the new regime

Your donation is still valuable, but it will not reduce your taxable income. The new regime allows only a limited set of deductions, and Section 80G is not one of them. 

If you have a specific fund or temple/trust in mind (for example, Karnataka Chief Minister's Relief Fund, ISKCON, Ramakrishna Mission, Tirumala Tirupati Devasthanams, etc.), tell me its name and I can check whether it has a valid 80G registration and, if so, what deduction category (50% or 100%) applies under the old regime.

Me:

Chief Minister's Relief Fund of Assam for the recent horrendous floods in Assam. Doesn't make sense to me: Income tax goes to Central Govt from where the govt allots flood alleviation relief to Assam(if at all). And here I'm directly making donations to the epicentre: it is about one govt agency over the other.

Chatgpt:

I think you've put your finger on a genuine policy trade-off, and many people have expressed the same concern.

From a public finance perspective, there are two different flows of money:

1. Taxes are compulsory payments into the Consolidated Fund. Once there, Parliament and the governments decide how the money is allocated across defence, healthcare, roads, disaster relief, pensions, etc.

2. Donations are voluntary payments that allow citizens to direct additional resources to a specific cause—in this case, flood relief in Assam.

Under the old tax regime, Parliament chose to encourage such voluntary giving by allowing a deduction under Section 80G for eligible funds such as a State Chief Minister's Relief Fund. The Chief Minister's Relief Fund is explicitly listed as an eligible fund under Section 80G (subject to the statutory conditions). 

Under the new tax regime, the philosophy changed. The government simplified the tax system by lowering rates while removing most deductions and exemptions, including Section 80G. The idea is that everyone pays tax on a broader base, without needing to track deductions.

So your argument is essentially:

> "If I'm donating directly to a government-run relief fund that the government itself has established, why should that be treated differently from tax?"

That's a perfectly coherent policy position. One could argue that such donations:

reduce the financial burden on the State,

reach the intended beneficiaries more directly,

and therefore deserve continued tax recognition even under the simplified regime.

On the other hand, the government's counterargument would be:

the new regime deliberately avoids distinguishing between "good" and "better" deductions;

if one deduction (disaster relief) is retained, many others (education, healthcare charities, research institutions, etc.) would also seek similar treatment, making the "simplified" regime more complex again.

So it is less a question of economics than of tax policy design.

In fact, if you donate ₹1,00,000 to the Assam Chief Minister's Relief Fund under the new regime:

the Government of Assam receives the full ₹1,00,000 for flood relief;

but your taxable income remains unchanged.

Whereas under the old regime, assuming the donation qualified for a 100% deduction, you would both help the relief effort and reduce your taxable income by the eligible amount.

Me:

I think this is sophistry. So, what has changed in the environment that the assumption of the old regime be disregarded? How can simplicity in tax calculation be an argument for such a change. You just need to change the algorithm, or use AI, or whatever. I mean this so frustrating.

Chatgpt:

I understand why you find it frustrating. And I think it's important to distinguish between an explanation of the policy and a justification for the policy. They are not the same.

The government's stated rationale is simplification, but that does not, by itself, establish that removing the deduction was the best policy.

In fact, your question can be reframed as:

> What changed between the old and the new regime that made it undesirable to encourage donations to disaster relief?

There are a few possible answers, but none is "because computers couldn't calculate it."

Simplicity isn't about computation

You're absolutely right that calculating one more deduction is trivial. Even in the 1980s, income tax software could do it.

When policymakers speak of "simplification," they usually mean:

* fewer categories of deductions,

* fewer eligibility disputes,

* fewer opportunities for tax planning,

* fewer documents to verify,

* fewer assessments and litigation.

So "simplicity" is primarily an administrative concept, not a computational one.

The real policy shift

The new regime represents a different philosophy:

> "Instead of giving tax incentives to influence people's behaviour, charge lower tax rates and let people make their own spending decisions."

Whether that philosophy is preferable is a separate question.

Your specific example is stronger than the general charity case

I think there's a meaningful distinction between:

* donating to a private charitable trust,

* donating to a religious institution,

* donating directly to a government-established disaster relief fund.

The last case is different because the recipient is itself a government fund established for a public purpose. One could argue that such donations supplement public expenditure in exactly the area the government would otherwise have to finance.

That doesn't prove they must receive a deduction, but it does make them a special category worthy of separate consideration.

Why might the government still remove it?

One possible line of reasoning is:

> "We don't want taxpayers choosing where public resources go. Taxes are collected centrally, and elected governments decide allocations."

In that view, if someone wants to help Assam beyond paying taxes, that's a voluntary act of philanthropy rather than a substitute for taxation.

Again, that's a policy choice—not a mathematical necessity.

Is your criticism unreasonable?

I don't think so. It's a legitimate policy criticism to say:

disaster relief serves an undeniable public purpose;

donations to government disaster relief funds reduce pressure on public finances;

therefore they should perhaps remain deductible even if many other deductions are abolished.

In fact, one could design a new regime that eliminated 95% of deductions while retaining only a handful—say, donations to national or state disaster relief funds, military welfare funds, or similar government-notified emergency funds. That would still be administratively simple.

So I would separate the issues:

Why was the deduction removed? Because the legislature chose a broad rule: almost all Chapter VI-A deductions disappeared under the new regime.

Was that the only way to simplify the tax system? No. The legislature could have retained a small number of narrowly defined deductions, including government disaster relief funds, if it had wanted to. Simplicity alone does not logically require their removal.

In other words, the change reflects a policy preference, not a technical limitation.

Your observation highlights a broader question: Should donations made directly to government disaster relief funds be treated differently from donations to private charities? Reasonable people can disagree on that, and the current law answers "No" under the new regime—not because the donation is less valuable, but because the regime intentionally removes almost all such incentives.

Me: 

To this above quote of chatgpt: "We don't want taxpayers choosing where public resources go. Taxes are collected centrally, and elected governments decide allocations", I asked this question to chatgpt:

Wow! Is this progression or regression in public participation in governance? I pay the tax, but I have no right to know where it goes? Its like a fire and forget type of missile.

Chatgpt:

That's a profound question, and it's one that political philosophers have debated for centuries.

I would separate two issues that are easy to conflate:

1. The right to know where your taxes go.

2. The right to decide where your taxes go.

These are related, but they're not the same.

In a representative democracy like India, the constitutional model is that citizens do have a right to know—through the Union Budget, state budgets, audit reports, parliamentary debates, the work of the Comptroller and Auditor General of India, and the Right to Information Act. What citizens generally do not have is an individual right to earmark their taxes for particular purposes. That power is exercised collectively through elected representatives.

Your concern, however, is slightly different. You're not saying:

> I want to divert my income tax to Assam.

You're saying:

> "After paying my taxes, if I voluntarily contribute additional money to a government disaster relief fund, why should the tax system stop encouraging that?"

That's a narrower and quite distinct proposition.

Has public participation increased or decreased?

Reasonable people can disagree.

One view is that the new regime represents regression in one specific sense: it reduces one mechanism by which citizens could be encouraged to support public causes directly. If tax incentives increase participation in disaster relief, removing them could reduce that form of civic engagement.

Another view is that tax policy should remain neutral, neither encouraging nor discouraging particular forms of giving, leaving charitable decisions entirely to individuals without tax incentives.

Neither conclusion follows automatically from economic theory; they reflect different ideas about the relationship between citizens and the state.

"Fire-and-forget" taxation

Your analogy captures a sentiment that many taxpayers express: once taxes are paid, individuals lose any direct influence over how those specific rupees are spent.

That is, in fact, a feature of most representative democracies. Taxes are pooled so governments can respond to changing priorities rather than being constrained by millions of individual earmarks. Imagine if everyone designated their taxes differently—one person only for defence, another only for education, another only for roads. Governments could struggle to fund essential but less popular services.

At the same time, there are countries and municipalities that experiment with participatory budgeting, where citizens directly vote on how a portion of public funds should be spent. Those experiments suggest that representative democracy and direct citizen participation need not be mutually exclusive—they can coexist.

So your question ultimately isn't just about Section 80G. It's about the balance between representative decision-making and citizen participation. The removal of the deduction can be seen as one small shift in that balance, but whether that shift is a progression or a regression is a matter of political philosophy rather than an objectively settled fact.

Me:

In other words, the govt is saying that your contribution should be totally altruistic. The govt is saying, 'We will decide where you tax goes: whether to make missiles, to education, to healthcare, or to natural disaster relief.' It would be instructive to know how much more/less has flown into Chief Minister's Relief fund (a representative case, say) after the new tax regime has come into force.

Chatgpt:

That's a very interesting empirical question, and it's exactly the kind of evidence that could inform the policy debate.

The hypothesis you're suggesting is:

> Removing the Section 80G deduction under the new regime may have reduced donations to government relief funds.

That's a testable proposition. But to answer it convincingly, we'd need data.

There are several possible outcomes:

Donations fell significantly. This would suggest that tax incentives were an important motivator, even for donations to government relief funds.

Donations remained roughly the same. This would suggest that most donors to disaster relief were motivated primarily by the cause rather than the tax benefit.

Donations increased. This could happen if the frequency or severity of disasters, public awareness, or corporate giving outweighed the effect of the tax change.

The difficulty is that many other factors influence donations:

* the scale of the disaster,

* media coverage,

* appeals by public figures,

* corporate social responsibility (CSR) contributions,

* growth in incomes,

* and the fact that many taxpayers still choose the **old regime** if it is more beneficial.

So simply comparing donations before and after the new regime would not, by itself, isolate the effect of removing the deduction.

However, a well-designed study could compare:

donations from individuals who switched to the new regime versus those who remained in the old regime,

or use statistical methods to estimate the impact while controlling for disaster severity and other variables.

Is the government asking for "pure altruism"?

In one sense, yes. Under the new regime, if you donate ₹10,000 to the Assam Chief Minister's Relief Fund, the tax system treats that as your voluntary charitable decision rather than something that merits a tax concession.

Whether that is good policy depends on the purpose one assigns to tax incentives.

There are two schools of thought:

Incentive view: Tax deductions are a legitimate tool to encourage socially beneficial activities, including disaster relief, research, education, and philanthropy.

Neutrality view: The tax system should raise revenue with minimal distortions, and governments should support public purposes through direct spending rather than through tax preferences.

Neither philosophy is universally accepted; different countries strike different balances.

The evidence would be valuable

I particularly like your suggestion of examining a representative Chief Minister's Relief Fund over time. If the data showed, for example, that individual donations fell sharply after taxpayers migrated to the new regime, it would strengthen the case for carving out an exception for government disaster relief funds.

Conversely, if donations were largely unchanged, policymakers could argue that the deduction was not materially influencing giving.

So the debate could move from principle to evidence.

I also wouldn't be surprised if this has not yet been studied rigorously in the public domain. Disaster relief donations are relatively episodic, and disentangling the effect of tax policy from the effect of the disaster itself is statistically challenging. But it is exactly the sort of question that economists of public finance would investigate using donation data, tax-return data (where available in aggregate), and natural experiments created by the introduction of the new regime.

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Idle mind is God's worship

 

Idle mind is Devil's workshop,

Idle mind is God's worship.

The train's window

 

The train's window

Is transparent glass.

Two hands,

One inside the train,

One outside,

Can see,

But can't join.

Meanwhile,

One hand is pushed away

By the motive force

Of the train.

One hand stays rooted

At the spot,

Due to force of gravity

Of the place,

And that of home.

The longing of belonging

 

The longing

Of belonging,

The gain,

Due to pain,

Is the measure

Of the heart sundered,

Is the treasure

Of being in love.

Regular in size, but an odd shape for a tablet?

The other day, I came across a tablet which had an unusual shape of a regular hexagon (see image below). I wondered why would a pharma company make a tablet that is hexagonal in shape. The intuitive thing of course was to give the tablet only distinctiveness. But was it the only answer? Perhaps there were more parameters working there. So, I decided to get more gyan on this from my friendly AI.

Me:

Wanted to know how do pharma companies decide on shape, colour, and size of tablets? I understand a tablet can't be more than swallowing power of a normal person. As also, the size would be proportional to the active ingredients inside the tablets. But what about shape and colour? For example, this tablet is in the shape of a regular hexagon. Most tablets are round. Capsules are cylindrical with both ends rounded. Some tablets are flattened cylinders. Any particular theory behind this? Also, why do pharma companies imprint names in the tinniest of fonts? Although, tablets are prescribed to all ages, but the propensity would be for the elderly, would it not? The ones with failing eyesight?

AI:

Good question — there's actually a fair amount of deliberate science (and some non-science, like marketing and patents) behind tablet design.

Shape

- Round/circular is the default because it's the easiest and cheapest to tool and manufacture — round punches wear more evenly, compress more consistently, and are less prone to capping/chipping during high-speed production. That's why most generic tablets are round.

- Oval/capsule-shaped (caplets) are chosen mainly for swallowability. An oval or elongated shape reduces the "throat profile" — the cross-section your throat has to pass — compared to a round tablet of the same volume, so bigger doses (500mg, 1g) are often oval rather than round.

- Unusual shapes (hexagons, diamonds, triangles, your tablet pentagon/hexagon) usually exist for brand differentiation and anti-counterfeiting. A distinctive shape is trademarkable and lets patients/pharmacists visually confirm "yes, this is the real product" at a glance. It also helps patients on multiple medications tell their pills apart by feel/sight, which reduces dosing errors. Sometimes shape is also tied to how the tablet needs to break (e.g., shapes with a scored line for easy halving).

- Capsules are cylindrical with rounded ends purely for swallowing mechanics — the rounded ends reduce friction and the risk of catching in the esophagus, and the gelatin/HPMC shell shape is somewhat fixed by the manufacturing process (dip-molding on pins).

Colour

Colour is almost never functional (no drug requires a particular colour to work). Reasons companies pick specific colours:

1. Brand identity and trademark — colour becomes part of recognizing "my medication," similar to shape.

2. Patient adherence and error reduction — hospitals and patients often rely on colour to distinguish drugs, especially when someone takes many pills. Studies show patients are more likely to stop taking a "generic" if it suddenly changes colour after a formulation switch, because they no longer visually recognize it as the "same" medicine, even though it's identical.

3. Psychological association — there's real research showing colour affects perceived potency and even effect: red/orange tablets are perceived as more stimulating, blue/green as calming or sedative, warm colours as more effective painkillers in placebo studies. Companies do use this in choosing colours for the intended perception (e.g., sedatives are rarely bright red).

4. Masking or matching the active ingredient's natural colour, or hiding slight batch-to-batch colour variation in the raw material.

Size

As you noted — dictated by dose (amount of active + excipients/fillers needed to bind and compress it) and by practical swallowability limits. Companies do try to minimize excipient bulk to keep tablets as small as possible, especially for chronic-use drugs.

The tiny imprint

This one's a genuinely reasonable complaint you're making. A few things going on:

- Regulators (like the US FDA) actually require an imprint code (letters/numbers, sometimes a logo) on most solid oral dosage forms specifically so tablets/capsules can be identified after they're out of the bottle — say, if someone's hospitalized and no one knows what pill it is, or in poisoning/overdose cases. This is a safety requirement, not vanity.

- The imprint is deliberately small because it has to fit on a tablet that's already sized to the minimum swallowable volume — there's very little surface area on something 6-10mm across, and the imprint has to leave room for the score line, logo, and not weaken the tablet's structural integrity (deep engraving can create fracture points).

- You're right that this creates an accessibility gap for elderly patients or anyone with low vision. This is a recognized problem in pharmacy practice — it's part of why pill identification is more reliably done via pharmacist/pill-identifier databases and apps (using shape + colour + imprint together) rather than by patients reading the imprint themselves. The imprint is really designed for someone else — a pharmacist, ER doctor, or poison control — to read, not necessarily the patient day-to-day.

So the short version: shape and colour are largely branding, trademark, and human-factors tools (recognition, adherence, error-avoidance) rather than anything to do with the drug's chemistry; the imprint is a regulatory safety requirement optimized for professional identification rather than patient legibility.

Me:

What is more amenable to ingestion into human systems? Tablets, or liquid potions? All things being equal: for example, degree of difficulty in manufacturing,  solubility, etc.

AI:

If you strip away manufacturing cost, shelf-stability, and practicality — and ask purely "which form gets the active drug into the bloodstream more efficiently" — liquids have the edge, for a fairly fundamental pharmacokinetic reason.

Why liquids absorb faster/more completely, in principle

A tablet, once swallowed, has to go through a sequence of steps before the drug can even reach the bloodstream:

1. Disintegration — the tablet breaks into granules

2. Deaggregation — granules break into fine particles

3. Dissolution — those particles dissolve into solution

4. Absorption — only the dissolved drug can cross the gut membrane

A liquid (true solution, not suspension) skips steps 1–3 entirely. The drug is already dissolved, so it's immediately available for absorption the moment it hits the stomach/intestine. This is why dissolution is often the rate-limiting step for tablets — pharmaceutical scientists spend enormous effort optimizing tablet disintegration/dissolution precisely because that's the bottleneck liquids don't have.

This is also why you'll notice:

- Pediatric and geriatric formulations skew liquid — faster onset, easier titration

- Emergency/acute-care drugs (e.g., some cardiac or antiemetic drugs) are often given as liquids, sublingual, or IV rather than solid tablets

- Bioequivalence studies use an oral solution as the theoretical "reference" against which a tablet's relative bioavailability is often benchmarked

Where tablets catch up or win, though

"All things being equal" doesn't fully hold in practice, because:

- Chemical stability: many drugs are far more stable as a dry solid than dissolved in water — hydrolysis, oxidation, and microbial growth are all faster in liquid form. This is why syrups need preservatives and shorter shelf lives, and why some drugs are literally impossible to formulate as stable liquids and only exist as tablets/capsules.

- First-pass metabolism: this is a systemic factor unrelated to formulation for most oral drugs — both tablets and liquids taken orally go through the liver first. (This only differs if you compare oral to sublingual/buccal/IV routes, which bypass first-pass regardless of solid or liquid form.)

- Dosing accuracy: a tablet delivers a fixed, precise dose every time. Liquids depend on the patient measuring correctly (a notoriously error-prone step — think of how inconsistently people use a kitchen spoon vs. a proper oral syringe).

- Gastric irritation and taste: some drugs are unpalatable or damaging to the stomach lining in concentrated liquid form and are deliberately given as enteric-coated or delayed-release tablets to control where and when they dissolve — something a liquid can't easily do. Modified-release tablets can actually outperform liquids for drugs where you want a slow, sustained absorption curve rather than a spike.

- Some drugs are insoluble or unstable in any aqueous vehicle at all, regardless of effort — solubility isn't just an engineering problem, it's dictated by the molecule's chemistry.

Net take

So the honest answer is: liquids win on pure absorption kinetics because they remove the dissolution bottleneck — but "amenable to ingestion" in the everyday clinical sense (accuracy, stability, control of release site/timing, patient convenience) often favors tablets, which is why they dominate the market despite the kinetic disadvantage. 

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. 

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:

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.

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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