(See Question) 

So, have you decided whether to stick to the door that you had initially chosen, or make a switch? Or perhaps you’re thinking that since 1 door is being opened, the probability of opening the door with a car behind would be 1/2 for each of the remaining 2 doors? Then think again!

Although we can make use of conditional probability to solve this problem, I will illustrate how to solve by using diagrams and lay-man explanation.

In the 3 situations below, the car is always in Door A, and we select different initial doors in each of the 3 different situations shown. 

Situation 1:

 

• Car is in Door A.
• You select Door A initially.

• Game host opens Door B to show you the car isn’t in B, and asks if you want to switch your choice.
• You decides to switch from Door A to C.

 

• Game host opens Door C, and you don’t win the car.

Situation 2:

 

• Car is in Door A.
• You select Door B initially.

 

• Game host opens Door C to show you the car isn’t in C, and asks if you want to switch your choice.
• You decides to switch from Door B to A.

 

• Game host opens Door A, and you win the car!!! 

Situation 3:

 

• Car is in Door A.
• You select Door C initially.

• Game host opens Door B to show you the car isn’t in B, and asks if you want to switch your choice.
• You decides to switch from Door C to A.

 

• Game host opens Door A, and you win the car!!!

So, from the illustration, you could see that the player switched in all three situations, and got to win the car in 2 out of 3. So, the probability of winning the car if you switch is 2/3, while the probability of winning the car if you stick to your initial choice is only 1/3.

So, switching is always a better option when you see it in a mathematical perspective. Get it?

This problem is actually called the "Monty Hall Problem", and it could be solved by using Bayes’ Theorem easily.

Extension: If you’re still interested until this point, do work this problem out.

Now, imagine there are 4 doors instead of 3, and the car is hidden behind one of the doors. The player chooses a door. The game host then opens some other door that is a loser. The player then switchs to another door. The game host then opens another as-yet-unopened losing door, different from the player’s current choice. Now, there are only two unopened doors left: the player’s current choice and another one. The player decides to switch again. What is his probability of winning the car?

Well, lets say you’re a lucky contestant in the final round of a game show that gives you the chance of winning a brand new sports car. All you need to do is to pick the right door out of 3 doors, and if the car appears behind the door that you have chosen, you would win. Sounds simple?

Here’s the actual situation:

Suppose the 3 doors are labelled A, B and C. The showhost will ask you to choose a certain door. You name the door of your choice (e.g. A), and the host will open one of the other two doors instead (e.g. C) to show you that there’s no car behind that opened door. He then asks you if you would like to change your mind and select the other unopened door (e.g. B) instead.  

Will you change your choice? Which door has a higher probability of having a car behind, or both have the same probability?  

Finally, another week has passed! Due to my busy schedule recently, I’ve not been able to blog as frequently as I wished to. Now, I’m working in the library again, with endless piles of homework waiting to be marked. The mundane marking has taken a toll on my half-asleep brain, so I’ve decided to take a break by surfing the net.

Anyway, I’ve found some interesting trivia when I was surfing the American Scientist Online site, and thought I would just post some of them here. Well, have fun figuring them out!  

Q1: In industrialized countries, what proportion of adults are affected by food allergies?

• A. 1 in 2,000
• B. 1 in 640
• C. 1 in 50

Q2: How much weight can a single gecko’s sticky toes support?

• A. Two apples
• B. Two bowling balls
• C. Two people

Q3: The average yawn lasts

• A. 4 seconds
• B. 6 seconds
• C. 7 seconds

Q4: Which of these has been levitated sucessfully using strong magnetic fields?

• A. a golf ball
• B. a frog
• C. a pizza

Q5: Natives of the Tibetan plateau are, in general, well able to cope with the thin air of their high-altitude homeland because:

• A. Their blood contains an especially high concentration of hemoglobin.
• B. They are able to pass air through their lungs at an especially rapid rate.
• C. They have notably low metabolisms, which require considerably less oxygen to support.

Q6: The precursor to HIV-1 (the virus responsible for the vast majority of AIDS cases) is found in which of these animals?

• A. chimpanzees
• B. African green monkeys
• C. baboons

Yeah, just 6 questions. Scroll below to see if you’ve got them right!

 

 

 

 

 

 

 

 

Ans 1: C. Food allergy affects 1 in 50 adults and 1 in 20 young children, and the numbers are rising: The incidence of peanut allergy doubled between 1997 and 2002. 

Ans 2: C. Theoretically, the 6.5 million hairlike stalks on a tokay gecko could generate 1,300 newtons of shear force.

Ans 3: B. Yawns also come in bouts, at intervals of about 68 seconds, on average. 

Ans 4: B. Andre Geim, a physicist at the University of Manchester, and his collaborators have levitated a live frog using a powerful superconducting magnet. With a sufficiently intense magnetic field, any diamagnetic material can be levitated. 

Ans 5: B. Tibetans can maintain very high respiratory rates while at rest. Andean natives, in contrast, respirate normally but show very high hemoglobin concentrations—two strikingly different human adaptations to life at very high altitudes.

Ans 6: A. The closest relative of HIV-1 is the simian immunodeficiency virus SIVcpz, which is carried by chimpanzees. 

 

Have a good weekend!!  

 

Photographs like this one above may be misinterpreted by many as a digitally manipulated night scene with thin streaks added in the background to simulate meteor shower. However, the lines are indeed created by the several bright stars in the night sky. Why are they lines instead of bright dots then?

"Star trails" is the term used to describe such lines that add interest to the otherwise boring sky. These star trails are caused by the rotation of our planet. Just imagine the sky above us is turning in a circular manner. Hence the distant stars will also be moving in some directions accordingly. The capturing of star trails is done by exposing the camera shutter long enough (means clicking and holding on to the shutter for a long time, i.e. 10 minutes for the above picture), so that as the stars move, their images will streak across the film (or in my case the CCD sensor).

Another interesting fact is that the North Star (or Polaris) is the only visible star that doesn’t seem to move a bit even as our planet rotates. So if the camera is pointed at the North Star and has its shutter exposed for a long period of time, you will probably see a lot of circular streaks of star trails, with a bright dot (the North Star) in the middle of these circles.

During my Cameron Highlands trip, I had the luck to see a night sky decorated with a blanket of stars. Hoping to capture some star trail pictures, I aimed my rangefinder into the sky with some leaves in the foreground. Sadly, the pictures I took turned out to be less than satisfying, and I only managed to salvage 2 shots.

 

This one is taken using at around 23 mm focal length, exposed for 20 minutes. Trails not really obvious due to light pollution.

I’ll be off to Phuket tomorrow, planning to enjoy the beach there for 3 days and then end off my last trip of these holidays with a 42 km Marathon. I’m going to bring my DSLR this time, hoping to get a better night sky there and capture more of such star trails.

When I was small, I was often intrigued by the wonders of nature. When I saw rainbows, I imagined a care-bear (Cheer-Bear) standing at one end flashing the rainbow from its belly. When I heard thunders, I looked up into the sky to see if there was a monster creeping out of the clouds. I also remembered asking my mum why the moon was following us when we walked home at night. Little did I know that most of these questions that I had have a lot to do with science.

We’ve always taken for granted the way nature works around us, without making an effort to find out how and why certain things happen in certain ways. Well, we could argue that there’s no point knowing, because we can’t change the phenomenons with such knowledge  (most of the time) anyway. But nevertheless, it’s always interesting to understand the explanations or theories behind them.

One of the more commonly asked questions include "What causes low and high tides?", but not all people can give a satisfactory answer without doing any research first. So, what do you think causes tidal effects on the oceans?

 

If your answer is the moon, then you’re right. First, we have to understand that all planets have gravity. The larger a planet, the more gravity it possesses. This explains why the smaller-sized moon’s gravity is only one-sixth that of Earth’s.

 

Although the moon’s gravity is significantly less than Earth’s, it does have some effect on the ocean on Earth’s surface. At the point where the ocean’s surface is closest to the moon (point A on diagram), the moon’s gravitational attractive force is able to pull the ocean towards itself. This gives rise to a high tide at the part of the Earth closest to the moon.

However, we all know that there are two high/low tides per day. This means that at any point of time, there are two high tides and two low tides happening at two different parts of Earth. Since there’s only one moon, where does this other high tide come from? Actually, the other high tide that is happening at the same time would be at the opposite side of Earth (point B), where the moon’s attractive force is weakest.

 

An illustration on how the ocean reacts to the moon as the moon orbits around Earth. Click on the illustration to view a larger image. 

As Earth rotates from west to east, the two bulges (high tides) tend to stay on the Earth-moon line. Further researching revealed that there are different types of tides (which have specific names and characteristics respectively). These tides happen according to how the sun and moon are aligned.

Images are taken from http://home.hiwaay.net/~krcool/Astro/moon/moontides/. Do read further if you’re interested!

Have you ever wondered why do stars twinkle instead of emitting a light of constant brightness? Common beliefs include that of "Stars are like sun, a ball of fire, therefore as the stars burn, the flames from the fire dance around and cause the stars to twinkle", but most of us would doubt the credibility of such explanations.

To explain why a star twinkles, let me use an analogy here. You fill up a bowl with water, and then submerge a coin into it. Use a finger to generate some water waves as you look at the coin through the water. You would probably see the image of the coin wobbling side to side through the ripples because water in the bowl refracts the path of light from the coin.

This is similar to how light travels from the star to our eyes. Most stars are very far away from us, well outside our Earth’s atmosphere. Our atmosphere is very turbulent, with streams and eddies forming, churning around and dispersing all the time. These moving pockets of hot and warm air act like lenses with different optical density, distorting and refracting the light from the star as it passes through the many layers of the Earth’s atmosphere before it reaches our eyes.

Image taken from http://www.enchantedlearning.com 

As a result, we perceive this continuous random refraction of the light (see picture) as "twinkling" of the stars. In contrast, if we view the same stars in outer space, we will not be able to observe the "twinkling" effect simply because there isn’t any atmosphere.

So, now that you know what causes stars to twinkle, can anyone make an intelligent guess why planets do not "twinkle" when viewed from Earth?  

I had time after I got home from camp on Saturday, so I bought 4 light bulbs for some experimental shoot. I had previously seen this idea on some photography galleries, and decided to try it out on my own.

 

This is how the lightbulb lits up. Nothing special.

 

And what happens when the glass is broken? It burns!

And with a little photoshopping, you get a clearer observation of how the fume diffuses.

Cool? Now, anyone can explain this phenomenon in terms of science?  

On Saturday, I went to Pulau Semakau with some colleagues and friends. Pulau Semakau is now a landfill area, and waste from various incineration plants will be transported to Pulau Semakau for land-filling. It is estimated that the landfill project will be completed in year 2040, and the government is now trying to control the amount of waste produced by urging the public to practise the 3 Rs: Reduce Waste, Reuse Things and Recycle Waste.

Ok, before this entry gets boring, lets get down to the more interesting part of this trip. I was there for the purpose of the intertidal walk.  When the tide is low, one can discover an interesting marine life  beneath the shallow water. Together with our guide, we walked about in ankle-deep waters to spot for crabs, nudibranchs and other interesting marine animals that are around.

Click on the pictures below to see a larger-sized image. 

 

The very first thing we spotted was this. A sea cucumber (yes, you can eat this)! Despite the name, sea cucumbers are actually animals and not plant/vege. They get tensed up and hardened when they sense danger. In fact, I touched it and it felt like a hard protective shield.

 

I almost didn’t want to take the picture of this hairy crab. Simply because it’s so hairy and doesn’t look like a crab at all. Ugly! haha..:P But yeah, I shot it eventually under the urging of someone.

 

This is the very venomous sea urchin. Colourful as it may seem, you should never go anywhere near it. Its venom can cause paralysis!

 

Jellyfish, another marine animal to be wary of! This jellyfish is known as the "upside-down" jellyfish, because it is usually seen floating upside-down (not in this pic though). Symbiotic algae can be found living at the undersides of the jellyfish, which help produce oxygen and thus allows the jellyfish to survive in oxygen-poor water.

Below are a few coral pictures that I’ve taken. I’m not too sure of the names, but I hope I get them right. 

 

A Favia coral. Each coral is made up of many tiny animals living together. This is called a colony and each animal is called a polyp (the green parts). The polyp has tentacles and it looks like a miniature sea anemone. Hard corals have a skeleton of calcium carbonate.

 

This should be a Maze coral (also hard). 

 

 

These are Sunflower mushroom corals, a type of soft coral. Soft corals are also colony of tiny animals called polyps. Unlike hard corals, they don’t have hard skeletons and the polyps are instead supported by a soft tissue mass. Out of water, soft corals often appear smooth because the tiny polyps are retracted.

 

Probably one of the ugliest corals! Looks like a piece of gigantic oily chicken/pig skin??! I seriously don’t know the identification of this piece of stuff. But it should be a kind of soft coral (I touched it).

 

Another Favia coral.

 

See what we’ve found? The Red Sea Star! It is huge, about the size of a 15 inch monitor screen! There are multiple black pores on its surface.

 

This is the underside of the Red Sea Star. the five lines are actually tiny tube feet that it uses to move about. One interesting fact about starfish.. they can regenerate lost arms!!

 

 

Cute? This is one of the marine creatures that I was hoping to find, nudibranch! (Joey, this is the nudi that I was talking about ) Nudibranch comes from Latin "nudus" meaning "naked", and Greek "brankhia" meaning "gills". These sea slugs are sof-bodied snails. They are carnivorous, feeding on sponges, hydroids, or bryozoans. Some are cannibals, eating other sea slugs or even members of their own species.

 

Looks like an underwater flower, but it is actually a Peacock anemone. Such anemones have a ring of shorter tentacles surrounded by longer tentacles. They come in a wide variety of colours. They create a tube into which they can retract when threatened. Thus, they are sometimes called Tube anemones. Careful.. these things sting too.

Phew, I guess that’s all that I have!! I hope you enjoyed reading this entry (as much as I writing it). Through this intertidal walk, I sure learnt a lot about these interesting sea creatures. It is good to note that there exists such a rich marine life in our small country. Want to continue having such a natural habitat for these marine animals in Singapore? Do your part then.. no littering and polluting the waters!

 

Edit: If you’re interested in such intertidal walks (or other types of nature walks), please visit www.wildsingapore.com for more information. There is a lot of information there.

Yesterday, before going for a dinner with my teacher friends, I met Dawn at Bishan Park because she wanted to learn how to shoot macro with her Canon digicam. Having been there before, I knew I wasn’t going to expect a lot of interesting insects, but I brought my camera along anyway. And I didn’t regret it because I’ve got my first bee in flight shots near the spa centre!

Bees are flying insects, closely related to wasps and ants. They are adapted for feeding on nectar (an energy source primarily) and pollen (for protein and other nutrients).

They have long proboscis (some sort of a tubular feeding and sucking organ) that enables them to obtain the nectars from flowers.

Could you see something yellow attached to the bee in the pictures above? The thing attached to its hind leg is actually called scopa.  It is simply a particularly dense mass of elongated, often branched, hairs that acts like a storage device to pack the pollen that the bee has gathered. 

Bees play an important role in pollinating the flowering plants. Usually, bees that are deliberately gathering pollen are the more efficient pollinators. In fact, some farmers intentionally raise bees to use them as pollinators for their crops.

Above is a freezing shot of a honeybee in flight. As it was a real pain to focus properly because the bee was hovering erratically. Much luck was needed to capture sharp images of flying insects, and I was quite pleased with this one.

And this is the last picture of the series. Here, you can really see it up-close. Look at the distinctive scopa on its hind legs!

Hope you enjoyed viewing.  

Want to know how the back of a dragonfly’s head looks like?

Pink hairy.

White hollow.

Cool?

 

Front: Like wearing helmet.

The head of a dragonfly is large and concave, and is located on a flexible neck that consists of six segments. On the first segment of a dragonfly’s head are three tiny "eyes", or ocelli, arranged in a triangle (refer to last picture). These are believed to help a dragonfly measure changes in the amount of light. Dragonflies have very good vision and therefore, rely little on their other senses. Their mouth is adapted for biting, making them efficient hunters. They have prehensile labium, extendible jaws, which can be extended forward from underneath the head faster than most prey can react, making their bite fatal to the prey (I saw how it works on tv before. It’s awesome!). Dragonflies also have a pair of short, tiny bristle-like antenna.

Source: http://www.scsc.k12.ar.us/2001migration/Projects/RoarkJ/