Illusion On the Water by Sentosa

Lily and I went kayaking by the shore of Sentosa on August 16, 2026. It is our second paddling trip there, the first time was more than 4 years ago, on March 19, 2022. 

During our 2hour 40 minutes, 9km paddling journey from Tanjong Beach to Labrador Nature Park, and return, we saw a group of swimmers swimming in the ocean, rowers in two row boats practicing, and the constant presence of many giant Shipps waiting for port clearance. There were birds as well, a collared kingfisher flying around the shoreline near Tanjong  Rimau, a white bellied sea eagle overhead. We paddled across Pulau Renggis near the Keppel island, and into Berlayar Creek -  no need to paddle though, the nature did the work, rising tide pushed us in, so we could just enjoy the surrounding - listening to bird chirps, and trying to locate them. We paddled along the shoreline of Labrador Nature Park before returning. 

swimming in the ocean

                                                                       Collared Kingfisher

white bellied sea eagle

                                                                            Rowing 

inside Berlayar Creek - looking out

Those were not the most interesting experience!

The most interesting and intriguing observation was about the movement of a giant ship NYK Line.

On the way to Labrador Park (northwest direction), we paddled away from the shoreline, toward the tiny islet Pulau Palawan. We noticed the giant ship NYK Line. As we got closer to the islet, we noticed the ship was moving in the same direction as we did. On the return, we saw that NYK was far away to the northwest of the islet. Our hypothesis was confirmed!

As we continued our return trip in the southeast direction, we noticed that NYK Line was moving with us again !? I realized that what we observed was optical illusion. 

I believed that the big ship was somewhere behind the islet in the southwest direction, anchored, i.e. not moving. But how could this illusion form?

One factor is the distance, the anchorage zone is about 400 meters southwest to the islet, and the islet is 200 meters from Sentosa shore. The other factor is that we were moving, paddling, our view angle changes and used the islet as a reference point. See illustration. I thought I got the physics (optics) right.

Paddling toward the islet Pulau Palawan

NYK position when we were paddling back to Tanjong Beach

                                                NYK Line followed us again on the return trip?!

Reason for the Optical Illusion

I uploaded the gif of the NYK and my illustration to Google. My reasoning is confirmed, and  the illusion has a scientific name  - motion parallax. 

Motion parallax is a visual cue that helps us perceive depth. When we move, nearby objects appear to move across our field of view much faster than distant objects. Our brains use this difference in apparent motion to estimate how far away things are.

It is something we experience constantly without consciously noticing it. The same principle is also important in technologies such as video games, computer graphics, and virtual reality, where it helps create the perception of three-dimensional depth.

What fascinated me was that I had encountered this phenomenon not in a textbook or laboratory, but simply by paddling a kayak around an island.

The optical illusion turned out to be the most interesting part of the entire paddling trip.

A simple observation became a puzzle. The puzzle led me to think about distance, movement, and reference points. I formed a hypothesis, tested it, and rediscovered an established scientific principle—one that I had encountered in a completely unexpected context.

That is one of the things I enjoy most about exploring nature.

I enjoy the sights and sounds, of course. But I also enjoy the questions that nature quietly presents.

Sometimes I notice something unusual.

Then I wonder why.

The curiosity leads to a mystery, the mystery leads to investigation, and the investigation often leads to a little discovery—sometimes in a field far outside my own expertise.

And that, to me, is part of the fun of exploring nature.

Explore Nature. Have Fun!

 

Appendix 

A. Here is the Google AI explanation of the observation in the GIF and my diagram:

Why the Ship Appears to Move with Your Kayak

What you are experiencing in your GIF is a classic optical phenomenon known as motion parallax:

• The Setup: The small green islet sits close to you (the foreground), while the massive NYK Line freight ship is significantly further out in the deep shipping lanes of the Singapore Strait (the background).
• The Illusion: As you kayak from right to left, you are actively changing your angle of view relative to the nearby islet. Because the islet is so close, it appears to shift backward (to your right) very quickly against the distant background.
• The Result: Because the ship in the background stays relatively fixed in your field of vision due to its extreme distance, the rapid backward movement of the nearby island makes the ship look like it is drifting or moving forward along with you toward the left.

The illustrtion is a fantastic, highly precise geometric breakdown of the illusion! Your diagram perfectly illustrates why it fooled you on the way out and revealed itself on the way back.

Why Your Diagram Explains It Perfectly

By tracking the intersection lines from the moving kayak through the edges of the stationary islet, your illustration beautifully maps out the changing sightlines:

• The Focal Point: As your kayak (the dots moving left) approaches and passes the islet, your line of sight has to swing backward to keep the islet centered in your vision.
• The Background Shift: Because the ship sits far behind that pivot point, the sightlines intersecting the islet project onto the distant background at a faster rate than you are actually moving forward.
• The "Anchored" Clue: Discovering that it happened in both directions is the ultimate proof of a stationary object. If the ship had actually been moving, it would have separated from the islet on your return journey. Instead, it stayed locked in that geometric dance.

Many ships anchor in that exact southwest zone of the Singapore Strait while waiting for port clearance, making them the perfect stationary backdrops for this exact parallax trick. It's a brilliant real-world observation and an excellent piece of diagramming!

B. Motion Parallax in applications

In video game design and virtual reality (VR), motion parallax is a critical tool used to create a sense of 3D depth on flat screens and prevent motion sickness in immersive headsets.

Here is how developers use it across different mediums:

1. 2D Video Games: Parallax Scrolling

In 2D games, developers stack art assets into independent, layered backgrounds that move at different speeds relative to the camera.

• Foreground layers: Move incredibly fast (e.g., leaves, lampposts passing close to the screen).
• Midground layers: Move at a moderate speed where the playable character usually resides.
• Background layers: Move very slowly (e.g., distant mountains, clouds, or stars) to simulate massive distance.

2. 3D Video Games: Camera Control & Scale

Modern 3D engines handle motion parallax automatically through the camera's field of view (FOV), but developers fine-tune it to manipulate player perception.

• Speed Perception: Placing objects close to the camera (like narrow canyon walls) increases the sensation of high speed. Wide open landscapes make the player feel like they are moving slower.
• Skyboxes: The sky and distant horizons are programmed to move perfectly with the camera's coordinates so they never get closer, creating an illusion of infinite distance.

3. Virtual Reality (VR): Head Tracking

In VR, motion parallax is the boundary between a highly immersive experience and immediate nausea.

• 6 Degrees of Freedom (6DoF): Modern VR headsets track your exact head movements in space. When you lean left or right, the virtual objects close to your face shift dramatically, while the background shifts minimally.
• Comfort & Realism: This real-time calculation mimics how our eyes naturally perceive the physical world. Without accurate motion parallax, your brain detects a mismatch between your inner ear (vestibular system) and your eyes, leading to severe motion sickness.

To help tailor this further, let me know:

• Are you looking for programming concepts (like how to implement a parallax script in Unity or Unreal Engine)?
• Would you like examples of classic games that pioneered this technique?
• Are you designing your own VR or game project?

Zugspitze Area

The Zugspitze, at 2,962 m above sea level, is the highest mountain in Germany. It is about 100km southwest from Munich. We went there with a guided tour on Sunday, July 19th, 2026, our second day in Germany.

Unfortunately it rained heavily in the morning when we got to the base of the mountain. Zugspitze was in the dense cloud. The tour guide was flexible, he suggested that we went to a charming small town nearby to wait out the rain - Garmisch-Partenkirchen.

Garmisch-Partenkirchen

It is a charming small town at the foot of Zugspitze.

The light rain there actually made this detour to the town very pleasant. There were few people in the streets. Walking slowly around town center, we appreciated the narrow streets,  biblical murals on many buildings, and  potted flowers on window sills or balconies. There are also quite a few churches.

The cloud started to breakup after lunch, and we drove to Zugspitze in a hurry.

 

Zugspitze

When we got there, the foothill was sunny but the summit was still clouded. Since the next cogwheel to the summit was, 45 minutes later, we watched the clouds at summit come and go. From time to time, I could see the summit clearly via my camera.

"

When we got off the cogwheel, before transfer to the gondola for the summit, we stepped out of the station. Looking south , the clouds broke up for a moment, the valleys, mountains, and remnants of glaciers  appeared.  No view of the north side of the mountain, especially the beautiful Eibsee, at the north foothill of Zugspitze. 

When finally reached the summit area, we were engulfed by clouds, could not see anything - from the south side or north side. We could not see Eibsee from above, we did not reach the real summit either even though we were only about 30 feet below it. The real summit is separated from the viewing platform by a "chasm". The steep drop-off and bad weather dissuaded us from climbing to the summit, a short distance away.

 

Summiting Zugspitze via Cogwheel on this day was disappointing. The only consolation was that we did see the stunning Eibsee on the way from Cogwheel  - the dark blue water, the light blue and white sandbars. One can not see these color combinations from lake level.

This was the best image of the summit we could see when we were near the summit -  less than 30feet below it

Eibsee 

Eibsee

We did not lingue at the Zugspitze summit area for long, we went downhill via Gondola and hiked on a small portion of the northeast side of Eibsee, with the Mountain in the background. It was sunny, and pleasant.

We hiked a short distance along the south shore of Eibsee before taking cogwheel to the summit. A different vista than that from north shore

Hindsight we might have enjoyed the trip more if we did not go up the mountain, but stayed downhill, and hiked around the lake on a 7.5 km trail. But it was what it was, we took what nature gave us, and enjoyed it as much as we could.

Note

Zugspitze needs a one full day trip. If we go there again, we will rent a car for two days at Munich, drive to the mountain in the early morning, climb the mountain, and rest/hike around the lake, and stop by Garmisch-Partenkirchen for dinner before returning

The Cannon Ball Tree Mystery

The fruit of the cannon ball tree is so distinctive that, after seeing it for the first time, I could immediately recognize the tree by its fruit. I have no such ability with most of the other trees and plants I encounter in Singapore.

The cannon ball tree, officially known as *Couroupita guianensis*, is not native to Southeast Asia. It is a deciduous tropical tree originally from the lowland rainforests of Central and South America. Because of its fragrant flowers and unusual, large fruits, it has been introduced and cultivated in many tropical parts of the world.

A cannon ball tree with flowers and fruit

In Singapore, cannon ball trees are fairly common. We see them at Fort Canning, Pasir Ris, West Coast Park, and other places. Because they are so familiar, I never paid much attention to their flowers or fruit.

That changed in November 2021.

The left tree has many flowers but no cannon balls, the right tree,
the right tree has many cannon balls, scarce flowers. Singapore Botanic Garden

A strange observation

We were at West Coast Park, where there are many cannon ball trees. I noticed something peculiar: quite a few trees were covered with cannon balls; this was in sharp contrast to  what I observed at Fort Canning , cannon ball trees there had few or no fruit. The trees with no fruit often had many flowers scattered beneath them. Later, I noticed exactly the same phenomenon at the Singapore Botanic Gardens, where two cannon ball trees stand right next to each other.

One tree was covered with cannon balls and had relatively few flowers.

The other was covered with flowers—but had no cannon balls.

We wondered why.

It became a little mystery.

The mystery follows us

This May, while walking along a trail at Pasir Ris Park lined with cannon ball trees, we encountered the same pattern again.

One tree had many cannon balls but relatively few flowers. Another had abundant flowers but no fruit. Other trees nearby looked more "normal," with a mixture of flowers and developing fruits.

This time, we also saw the inside of a cannon ball for the first time.

The mystery deepened.

Then, as often happens with questions that don't have immediate answers, we forgot about it.

Until last week.

We walked past the two cannon ball trees at the Singapore Botanic Gardens again. There they were, still showing the same striking contrast: one covered with flowers, the other laden with cannon balls.

I mentioned it to Lily.

She challenged me: "Why don't you find out?"

So I did.

A broken fallen Cannon Ball at Pasir Ris 

A normal Cannon Ball Tree

The mystery begins to unravel

A little online research suggested that there are at least two possible explanations for the difference we observed.

The first is simply different flowering and fruiting cycles.

Tropical trees do not necessarily follow the same seasonal rhythms as temperate trees. Individual trees can have different internal cycles. One tree may be producing flowers while another is developing fruit. Even trees growing side by side, experiencing essentially the same weather and soil conditions, may not be synchronized.

This could explain some of the differences we saw.

But it doesn't completely explain the two cannon ball trees at the Singapore Botanic Gardens. They are right next to each other, yet one repeatedly produces abundant flowers while the other produces abundant fruit.

That raises another possibility: individual differences in reproductive biology.

Perhaps the flowering tree has some characteristic that makes it produce flowers but rarely develop fruit. A genetic difference, reproductive incompatibility, or another biological factor could potentially be involved.

But this is only a hypothesis. Without examining the trees or conducting botanical studies, we cannot know whether genetics—or something else—is responsible.

And that uncertainty made the mystery even more interesting.

What I learned about cannon ball trees

My curiosity about the mystery led me into the fascinating reproductive biology of the cannon ball tree.

Each flower contains both male and female reproductive organs. The flowers have numerous stamens that produce pollen, as well as a central ovary and stigma capable of receiving pollen.

Yet having both reproductive organs in the same flower does not necessarily mean that a tree simply fertilizes itself. Cannon ball trees rely heavily on large bees for pollination. Their flowers even produce different types of pollen: some fertile and used for reproduction, and some apparently serving as nutritious food for visiting insects.

Another fascinating fact is the length of the fruit-development process.

Once pollinated, a cannon ball fruit can take roughly **12 to 18 months** to mature and eventually fall from the tree, and under some conditions it can take even longer.

Suddenly, those cannon balls hanging from the branches looked quite different to me. They were not simply fruits sitting on a tree—they represented a reproductive process that had been unfolding for well over a year.

Curiosity creates mystery

Looking back, I realize that I created this mystery simply by noticing something that most people would probably walk past.

I saw two trees that looked different and asked: Why?

That simple question took me from an ordinary walk in Singapore to tropical botany, pollination, reproductive biology, flowering cycles, and the remarkable life history of a tree from South America.

I still don't know exactly why those two cannon ball trees behave so differently.

And perhaps that's part of the fun. A simple observation turned into an exciting puzzle.

Only when I became curious enough to look deeper did I discover how much wonder was hiding behind something I had walked past many times before.

Curiosity creates mystery.

And sometimes, mystery is the beginning of discovery.

Notes 

This post is a polished version by chatGPT (with minor edit) of my original full draft 

Here is chatGPT's comment on the original draft:

Absolutely. I think the strongest aspect of this essay is the **curiosity-driven structure**: you notice something unusual, it becomes a mystery, you investigate it, and the investigation leads to a broader appreciation of plant biology. I would make that progression more prominent and reduce some of the technical detail that interrupts the story.

One important point: I would also **soften the Google AI explanation** about the “genetically barren” tree. The essay currently presents that as an explanation, but the evidence you describe doesn't establish that this particular tree is triploid or genetically defective. It is better presented as a hypothesis rather than a conclusion.

I particularly like the ending **“Curiosity creates mystery. And sometimes, mystery is the beginning of discovery.”** It connects nicely with the broader theme that appears in several of your nature essays: you don't just photograph what you see—you **notice something unusual, ask why, and then investigate it**. 

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Appendix 

1. original full draft

2. chat with Gemini

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Original Draft of the post

We saw the cannon ball trees for the first time at Fort Canning in July 2021. 

The tree's fruit, the cannon ball, is so unique and relatable, I am able identify it by name after the first exposure. I have no such ability with all other flora in Singapore.

However cannon ball trees are not native to Southeast Asia.

The cannon ball trees' official name is Couroupita guianensis, is a deciduous tree in the flowering plant family Lecythidaceae. It is native to lowland tropical rainforests of Central and South America. It is introduced to, cultivated in many other tropical areas throughout the world because of its fragrant flowers and large fruit.

We see cannon ball trees at many places, Fort Canning, Pasir Ris, West Coast Park, ... It is so common, I did not pay much attention to their flowers and fruit. 

Nevertheless I did notice a peculiar phenomenon about the tress early on, after sighting of the trees at a second location, West Coast Park, later in November 2021. What was unique here at west coast park was that, there are many cannon ball trees, and quite a few of them have many cannon balls, compared to none or only one cannon ball from cannon ball trees at Fort Canning area, with many fallen flowers.

I observed the same phenomenon at Singapore Botanic Garden, where two cannon ball trees are right next to each other. One has many cannon balls, some flowers, the other is covered by flowers but no cannon balls.

We wondered why. It was a mystery to us.

This May, we walked along a trail  with cannon ball trees lined on one side of it, at Pasir Ris Park. Interestingly we observed the same phenomenon, one tree has many cannon balls, but few flowers, another has many flowers no cannon ball! The other cannon ball trees are normal, which have some cannon balls, some flowers. We also saw the inside of the cannon balls this time for the first time.

The mystery deepened for a moment. However we forgot about it afterwards.

Last week, when we walked by the two cannon ball trees again, saw the same two cannon ball trees, one has only flowers, one has a full tree of cannon balls, just like what we observed numerous time before. I wondered aloud to Lily. She challenged me to find out the reason.

I did a bit online research. The following is what I found out.

The Mystery Explained by Google AI

There are two possible (simplified) reasons for what we observed (see Appendix for  expanded discussions).

1) Mismatched Timelines  - this does not apply to the two SBG next to each cannon ball trees

Unlike temperate trees that bloom simultaneously due to rigid winter-to-spring temperature changes, tropical rainforest trees often follow individual internal clocks. Even when planted side-by-side in identical soil and weather, individual cannonball trees can be completely out of sync with each other. When one finishes fruiting and drops its crop, it will swap phases—quieting down its fruit production and exploding into bloom like its neighbor.

2) SBG Cannon Ball trees: The Left Tree is "Genetically Barren" (Triploid or Defective), The Right Tree is normal

In botanical collections like the Singapore Botanic Gardens, individual trees are sometimes accidental clones or possess minor genetic mutations. The Left Tree: It likely has a chromosomal defect (such as triploidy) or a mutation in its reproductive organs that renders its fertile pollen or ovules completely non-functional. Because it never sets fruit, it avoids the massive metabolic drain of growing heavy cannonballs. It hoards 100% of its nutrients every year exclusively for flower production, turning it into a perpetual blooming machine. The Right Tree: It has perfectly healthy, normal genetics. It easily accepts pollen carried by bees from the blooming left tree, allowing it to stay constantly laden with heavy, growing fruit.

Because of the answers from Google AI, I had more questions about the plant biology related to reproduction, which led to the following secton.

Cannon Ball trees and plant biology

1. Cannon ball trees are bisexual ,meaning each individual flower contains both male and female reproductive organs.

• Male Organs: The flowers feature hundreds of pollen-producing stamens arranged in a unique, hood-like structure.
• Female Organs: The centre of the flower contains a functional fertile ovary and stigma to receive pollen.
• Pollination Strategy: Despite having both sexes in one flower, the tree relies heavily on large bees for cross-pollination. Interestingly, the flower generates two types of pollen: fertile pollen to reproduce and sterile, nutritious pollen to feed the visiting insects. [1, 2]
• It takes 12 to 18 months for a cannonball flower to develop into a mature fruit and naturally drop off from the tree. In some environments, it can take up to 24 months.

[1] https://www.nparks.gov.sg

[2] https://www.namograndcentralpark.com

2. The vast majority of flowering plants (angiosperms) are bisexual. Approximately 85% to 90% of all flowering plant species worldwide produce perfect, hermaphroditic flowers containing both functional male and female reproductive organs

3. Trees distribute their sexes slightly differently than smaller herbaceous plants. Globally, around 75% of all tree species are bisexual. Trees rely slightly more on wind-pollinated, single-sex configurations (like monoecy found in pines, birches, and walnuts) because their height grants them better access to the wind.

Curiosity Creates Mystery

I created this cannon ball tree mystery because I noticed the obvious differences in some cannon ball trees and wondered about it.

Only when I was interested enough to dig deeper into the reasons, I find wonder. 

A simple observation turned into an exciting puzzle!

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2. Chat with Gemini

Prompt 1 - i saw two cannon ball trees which are next to each other, one has many flowers but no cannon ball, the other has many cannon balls, few flowers. what caused this phenomenon, see the photo attached

Google AI reply

What you are seeing is a textbook example of asynchronous reproduction and energy allocation in tropical trees.

Even though these two cannonball trees (Couroupita guianensis) are growing right next to each other, they are simply in different phases of their reproductive cycles. [1]. The phenomenon is caused by a combination of biological factors:

1. High Resource Consumption of Fruits

Developing a "cannonball" fruit is an incredibly demanding task for the tree. These massive, woody spheres can grow up to 25 cm in diameter and take 12 to 18 months to fully mature and ripen. [2, 3]

• The Tree on the Right: It has heavily invested its stored nutrients, sugars, and energy into sustaining the crop of large fruits you see hanging from its trunk. Because its energy reserves are maxed out by fruiting, it has minimal resources left to produce new flowers.
• The Tree on the Left: It currently has no fruits draining its energy. As a result, it can channel all its accumulated sugars into a spectacular, high-energy mass-flowering phase. [4]

2. Asynchronous Phenology (Mismatched Timelines)

Unlike temperate trees that bloom simultaneously due to rigid winter-to-spring temperature changes, tropical rainforest trees often follow individual internal clocks. Even when planted side-by-side in identical soil and weather, individual cannonball trees can be completely out of sync with each other. When one finishes fruiting and drops its crop, it will swap phases—quieting down its fruit production and exploding into bloom like its neighbor.

3. Low Pollination Success Rate

The tree on the left has thousands of flowers, but only a tiny fraction of them will ever turn into cannonballs. Because cannonball flowers produce no nectar and rely entirely on large, specialized native bees (like carpenter bees) to transport fertile pollen between separate trees, many flowers fall off unpollinated. The tree on the right likely had a highly successful visiting pollinator phase a year ago, while the tree on the left is actively trying to attract pollinators right now. [2, 4, 5, 6]

[1] https://www.gardenia.net

[2] https://www.facebook.com

[3] https://www.facebook.com

[4] https://www.facebook.com

[5] https://heritagetrees.nparks.gov.sg

[6] https://www.nybg.org

Prompt 2 - The two trees are in Singapore Botanic Garden, I see the same phenomenon, every year, never see the left tree has cannon ball on it except one time I saw one cannon ball; the right tree always have many cannon balls on it, not too many blooming flowers. It does not seem to be Mismatched Timelines.

Google AI reply

Thank you for sharing that crucial observation. Since this pattern is consistent year after year, it completely changes the diagnosis.

When one tree continuously bursts with flowers but almost never sets fruit, while its neighbor constantly bears fruit, you are witnessing severe self-sterility and a localized breakdown in genetic compatibility. [1]

The phenomenon is caused by a few specific factors:

1. Late-Acting Self-Incompatibility (LSI)

The cannonball tree (Couroupita guianensis) possesses a strict genetic mechanism called late-acting self-incompatibility. [1]

• Even though the flowers are bisexual, a tree cannot fertilize itself. If a bee transfers pollen from the left tree back onto its own flowers, the tree recognizes its own DNA inside the ovary and actively aborts the fruit in its first month. [1]
• The single cannonball you saw on the left tree was likely a rare fluke where a pollinator managed to bring compatible pollen from a third tree located much further away.

2. Clonal or Mismatched Genetics

For successful cross-pollination, the left tree must receive pollen from a genetically distinct individual. If the two trees in the Singapore Botanic Gardens are too closely related—such as being grown from seeds of the exact same parent fruit or cloned from cuttings—their genetic compatibility will be severely limited. [1]

• The Right Tree: It likely has a slightly different genetic makeup that allows it to accept pollen from the left tree (or other cannonball trees in the area), converting its blooms into fruit. [2]
• The Left Tree: It is stuck in a genetic "dead end." It cannot accept its own pollen, and it cannot accept its neighbor's pollen. Because it fails to set fruit, it doesn't deplete its energy reserves, allowing it to spend 100% of its resources on massive, continuous flower displays every year. [1]

3. Asymmetric Pollinator Behavior

The Carpenter Bees (Xylocopa spp.) in the gardens are highly efficient, but they follow the rewards. Because the left tree always has an overwhelming density of flowers, bees will heavily forage on it. [2]

• When a bee moves from the left tree over to the right tree, it carries a heavy load of the left tree's pollen, easily fertilizing the right tree.
• However, because the right tree has very few flowers, bees rarely fly from the right tree back to the left one. Even if they do, the genetic incompatibility blocks the left tree from forming fruits anyway. [1]

[1] https://www.researchgate.net

[2] https://ancienttrees.app

[3] https://heritagetrees.nparks.gov.sg