Recently, astronomers discovered an “old star” (100 billion years old apparently) that was giving birth to “new planets”…this is what a scientist had to say:

“We currently understand planet formation to occur around stars when they are very young…As such, we would never expect a star to undergo planet formation late in its life as the necessary conditions are not present.”

Now a statement like this leads me to believe that their knowledge is only speculation to begin with…obviously the conclusions that they had previously come to were just blown to bits by nature itself. I wonder how many millions of dollars we’ve paid these scientists as a collectivity [sic] to come to the “accurate conclusions” they’ve come to in various fields. And when you look at the overall benefit to mankind in these things, one must wonder just why it’s done at all.

It’s this very thing which drives me crazy - that’s the whole point of science. We don’t know everything, nor do we scientists ever claim to. As countless people before me have said - theories in science are almost always evolving. New observations are either fitted into the existing framework or we develop new theories which do include and explain these observations. Scientists love it when discoveries disprove old theories - it often means there’s a whole new area of science to explore, with who knows what results.

And even then, theories are rarely “blown to bits”. Instead, we realise that our existing theories are only part of the picture. Einstein’s Theory of Relativity didn’t disprove Newton’s theories of motion. Instead, they showed us that Newton’s laws are the “low speed” approximation to a bigger theory. Newton was perfectly right - unless you happen to be going near the speed of light! I’m sure our theories of planet formation will evolve accordingly.

As for “the overall benefit to mankind” - How about antibiotics and the countless other medicines? Chemotherapy? The internet? Solar power? And sure, maybe understanding planet formation doesn’t feed the hungry but it’s part of learning how the universe works, and from that who knows what we’ll discover! (Lasers were initially a scientific novelty - now look at them!) As for evolution - how dramatically did it change our understanding of life on Earth! But Billy, if you’d prefer not to use your internet, TV, car or medicines - feel free!

But this is the sort of thing that religion so often blinds people - the fact that the universe is an amazing, incredible place regardless of whether or not a God exists, and that science is helping us to appreciate and utilise the beauty of it.

Not a loaded question, but pure curiosity: How many lives has the Bible saved over the last 200 years, compared to advances in science over the same period? (And how could you estimate either?)

So what gets people so impassioned? Here’s the problem:

A plane is standing on a runway that can move (some sort of conveyor belt). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?

Or, a better phrasing is this:

A plane is standing on a runway that can move. The plane moves in one direction, while the conveyor moves in the opposite direction at the plane’s take off speed. Can the plane take off?

Stop and think about it. Then, read on

My first answer was…no. My (incorrect!) thinking was that it’s the speed of the air over the plane wings that provides the lift for a plane to fly. Hence if you were on a backwards moving conveyor belt, so that you weren’t moving relative to the air, there would never be any lift no matter how fast you went and you could never take off.

But I “misread” the question - I’m right in part - we’ll all agree that if a plane is not moving relative to the air, then it cannot take off. (It’s the motion of air over the wings that gives it lift.) But what this question is asking is really this: Can a conveyor belt stop a plane from moving and accelerating forwards through the air? Or, another way, can a plane on a conveyor belt move forward through the air, no matter how fast the belt is moving?

The answer is yes - it can and will.

Let’s explain this three times -first, with facts, second with physics, then finally building up a logical argument with more details. I’m using ideas from a variety of sources, including Straight Dope, doesn’t depend on speed, for all intents and purposes.)

So, finally, to our plane. The wheels on a plane are only used for rolling or braking - they’re not “powered” in anyway, just like a rollerblade. Instead, a plane is able to accelerate quite independently of the ground (e.g., in mid air!), by using its engines or a propeller. No matter how fast the conveyor belt is moving, I can use a small amount of my thrust to overcome the friction there (just like the roller blades), and the rest goes into accelerating the plane. That means that the plane can and will start to accelerate forwards, eventually reaching take off speed. Again, in terms of forces, the only forces acting (horizontally) on the plane are the thrust from the engines and a tiny bit of friction from the imperfect wheels. It must move forward, by the laws of physics, and so will take off.

Just remember, that people who say a stationary plane can’t take off are absolutely right! But that’s not the key to this question - it’s whether a moving conveyor belt can stop a plane. And, it turns out, it can’t. This is really tough to get your head around at least in part because the problem is badly worded. Both sides have valid points, you’ve just got to agree on the problem. (In particular, the phrasing that the “belt moves at the same but opposite speed as the plane” - as the plane compared to what? Bad question!)

And the final words, of course, comes from Mythbusters who showed the plane can take off. It’s not a perfect experiment, but the basic idea is correct and shows the correct physics. (A moving tarp is a pretty good approximation to a conveyor belt - even if you can feel the ground through it, that shouldn’t change the friction much! The ground is still “moving”.)

I hope that helps clear things up!

(At this point, you really should watch the video, but read on regardless!)

The argument (according to the curricula authors) against the tried-and-true methods is that although most of us can “do” them (eventually) it can take a while to learn and not everyone understands why these methods work - the mathematical insight may be lost to the algorithm.

Instead, they suggest using more “intuitive” methods. One option for multiplication is the way most people do maths in their head, except on paper. Using their example, to multiply 26 x 31, you write it as 20×31+5×31+1×31. Then you can quickly work out 10×31=310, and double and halve it to get 20x and 5x. Finally, you add it all together and you’re done. It’s good because it’s very clear what you’re actually doing - what multiplication actually means, something which can easily get obscured in the traditional method. But I would have to think it would also be slower on paper - and probably more prone to making mistakes.

A compromise is the “partial products” method, where you do keep track of what you’re multiplying (e.g., in 26×31 you don’t multiply 2 by 3, but 20 by 30.) Finally, there’s the “lattice method” (which I read about when I was much younger in a fantastic coffee table book “Oddities”), which is very cool from a geek perspective, and useless otherwise.

So what should be taught? Certainly, some of these methods are ridiculous, but the basic idea isn’t. One Big Issue is calculators (I think there’s a whole separate post there). Most mathematicians go apoplectic when this comes up, but I think there’s points on both sides. You could argue, why bother teaching multiplication at all if a calculator can Just Do It? Realistically, I don’t often multiply by hand. Aside from arguments like “you won’t always have a calculator” (which is still important (think shopping!) but I don’t feel key here) in maths you need to develop your skills and, if you like, intuition for how things go together, and how to approach questions. Problems arise when students assume every problem can be solved just by sticking it into the calculator (and this gets “worse” with graphics calculators!) - as soon as a problem is out of the ordinary, I’ve watched students spend more time hunting for a possible equation solver in their calculator than it would have taken to solve by hand!

I can’t provide data, only anecdotes, but I’d think that if you never learned how to multiply, you’d find the more complex skills which build on the basic ideas much harder. And for just the sheer number of times you need to multiply, and for how much of other maths it underlies, it’s just such a valuable skill.

What about intuitive vs algorithmic approaches? I think the word “intuitive” is a bad choice, actually - really what they’re advocating is “guess and check” methods (”10 13’s fit into 200, subtract them off and we’re left with 70. At least one 13 fits in 70, etc) It helps build that deep understanding of how maths works, but I’d argue the method itself really isn’t “intuitive” - just frustrating after you understand the principles. Interestingly, when I tutor I always emphasise understanding rather than doing - but at the same time, I encourage students to follow procedures (e.g., for differentiation) at the expense of quicker “guess and check” shortcuts, because it drastically reduces errors. (Again, another post I think).

Again, I think multiplication is important enough to justify the proper algorithm. Division, though, I’m less certain on. I’ve learned long division, only ever used short division, and even that I use only rarely these days. I’d be tempted to say the guess-and-check understanding of division might be sufficient.

And, of course, all these arguments extend to other areas of school as well. I don’t remember most of what I learned in primary school - names of explorers, poems, etc. But was the “learning how to learn” more important than the content itself? (I generally have little interest in games like Trivial Pursuit, preferring games that require skill than can be developed rather than knowledge that you either have or you don’t. I guess I feel the same about school )

So I ask again, what do you think should be taught in primary school?

I’ve decided that there are already enough people commenting on science, and I can’t really add anything. But more and more, I’m interested in the perception of science, science education and just neat science problems that don’t necessarily have any application but are still cool

So that’s what I’m going to swing this blog towards - and I hope it will be all the more interesting because of it.

The gist is that you can dissolve more of the powder in hot water than in cold (just like dissolving sugar or salt - try dissolving as much as you can in a cup of cold water, then add some more, microwave and stir. It’ll all go in!) Then when it cools down, that extra dissolved powder wants to come out and solidify. But this requires a trigger to get things started - a crystal, a sharp knock, something. That lets you do all sorts of fun things (like the video shown above!) You can see the tower I made in my photo here. (You can also see - a mixture of corn flour and water (which makes a slime like mixture), some out of date eggs which I was trying to crush in my fist (you can’t with one hand), and some cream (which was for cocktails while I worked ) )

Unfortunately, I can’t quite get it right - either I haven’t dissolved enough powder, and the mixture won’t solidify when cooled and triggered. Or, I’ve added too much and it solidifies prematurely. But if at first you don’t succeed, try, try and try again! I’ll post my final recipe when I’m done!

(Of course, reading it, I couldn’t help but at least consider which way the causality runs here. It’s the old problem - correlation doesn’t imply causation. It could be the cat visits them because he senses they’re dying; but it could also be the cat, for example, aggravates their sinuses and tips them over the edge! I think that’s pretty unlikely though!)

Not convinced?

I can’t really imagine how water could act as a fuel directly, and their explanation that “The internal converter extracts electrons from the fluid molecules and provides a steady stream of electricity to generate power for the calculator.” is vague to say the least.

I can only assume that it works like an ordinary battery and has something like zinc and copper electrodes that, in the presence of water, are slowly corroding and freeing electrons to power the calculator. If this is the case, the calculator would be powered by nothing more than a built in battery, using water as an electrolyte, and will eventually stop working. You wouldn’t be “extract[ing] electrons from the fluid molecules”, and to say that it is “earth friendly” and “powered by most any liquid” is misleading to say the least, and pseuodoscience at the worst - not at all up to the usual standards of Steve Spangler Science! (Which just has really cool stuff!)

In the interest of upholding my scientific dignity (and when a bit of googling didn’t immediately turn up better explanations) I’ve rattled off an email to Steve Spangler Science, and we’ll see what happens!

The PhDComics guy, George Chan, is coming to Australia in September. And I’m planning to be away, travelling around the Northern Territory doing science shows. I mean, the latter is good, but I’ve been wanting to see him for YEARS! *sigh*

Apparently he’s going to be at UQ on the 20th of September. If you’re a Brisbane person, definitely worth checking out. If you’re in the USA, just invite him!!!

Three brilliant mathematicians have been kidnapped by Dr Evil, who is forcing them to play the Hat Game! He lines them up, blindfolded, one after the other, facing a wall, so that C can see B and A, B can see A, and A can see nothing:

| A B C

He explains (despite Scott’s protests…) that he has two white hats and three blacks, which he will put on the mathematicians. And, he promises to let them go if at least one person can guess their hat colour correctly. But, he warns them, if anyone guesses incorrectly, he’ll have them all killed anyway.

Version 1:

Simply put, will the mathematicians be able to escape? How should Dr Evil arrange the hats?

Version 2 (leading questions):

When he removes the blindfolds, mathematician C quickly pipes up his hat colour. What was it?

Dr Evil, thinking it could just have been a lucky guess, blindfolds them again and gives them new hats. This time, when he takes off the blindfolds, there’s a pause - and suddenly mathematician B announces his hat colour. What was it?

Frustrated, Dr Evil blindfolds them again and changes the hats. Whipping off their blindfolds, he giggles evilly while they sit silently. Then, mathematician A happily announces his hat colour. What was it?

(Just for the record, Dr Evil threw them all into a pool of sharks with laser beams on their heads anyway.)

Danger lies before you, while safety lies behind,
Two of us will help you, whichever you would find,
One among us seven will let you move ahead,
Another will transport the drinker back instead,
Two among our number hold only nettle wine,
Three of us are killers, waiting hidden in line.
Choose, unless you wish to stay here forevermore,
To help you in your choice, we give you these clues four:
First, however slyly the poison tries to hide
You will always find some on nettle wine’s left side;
Second, different are those who stand at either end,
But if you would move onward, neither is your friend;
Third, as you see clearly, all are different size,
Neither dwarf nor giant holds death in their insides;
Fourth, the second left and the second on the right
Are twins once you taste them, though different at first sight.

The catch is that the third clue tells us that “neither dwarf nor giant” bottles are poison - and we’re not told which of the seven bottles they are.

So, I started wondering - what, if anything, can we deduce from this riddle? It’s actually a neat little problem, with a clever problem solving twist. Have a go yourself, then read on for my solution and how it connects to one of my favourite logic puzzles!

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