Death by Fall? Not for a Squirrel.

Sneaky little buggers
(http://www.telegraph.co.uk/earth/earthnews/9699330/Ash-dieback-mistaken-for-squirrel-damage.html)

You've probably come across a squirrel at some point in your life.

Those furry little hyper-energetic creatures that dart hither and tither like a cat chasing a laser pointer. You know what I'm talking about.

Infamous for scurrying about in search of nuts to nibble on, most squirrels are tree dwelling species, and reside at significant heights.
With the advent of urban architechture, squirrels have also taken to bunking in urban homes and attics, settling on roofs and terraces, much to the annoyance of some of it's occupants.

But constantly living and scurrying about at heights has its dangers - specifically falling.
Now most mammals dread falls, but squirrels seem to risk them all the time? Why? Surely falling is bad for them too, right?

Wrong.
Let's see why.

First we have to understand a bit about falling objects, and the physics behind them.
In middle/high-school class, you've had to calculate the velocity of an object falling from a certain height.
But out in the real world, we have to take into account something we consistently ignore in problems - Air resistance. 

Any falling object has two forces acting on it while it falls.

• Gravity
• Aerodynamic resistance or Drag

But while the gravitational force is constant throughout it's fall, this drag increases with increase in (the square of) the velocity.

So as the velocity increases, there comes a point when the force of drag is equal to the pull of gravity. 
Since the net force on the body is zero, the body will move at a constant velocity. 
This constant velocity is special for any falling body, and is known as its terminal velocity.

No object will fall faster than it's terminal velocity, no matter what height it is dropped from.

Now, back to cute furry little things.
Squirrels, since they are small and light, means they have comparatively little pull from gravity, and since they have stretchy bodies and puffy tails, they experience a lot of drag. This means that their terminal velocity is actually quite low, and squirrels can survive impacts of that velocity.
ringing it all together. Terminal velocity is the fastest that an object will ever fall, no matter what height it is dropped from. Squirrels (unlike most other mammals) can survive impacts at their terminal velocity.

I believe I can fly....
 (http://www.stephaniegallman.com/2010/05/day-186-unwelcome-house-guest.html)

Which means no matter what height you drop a squirrel from, it will probably survive.
Though don't try flinging squirrels out of buildings just yet.

Cookie Science?

On the interplus, I came across an article from a food blog called the Food Lab, written by Kenji Lopez-Alt. The post I was interested in was about finding the recipe to create the optimal chocolate chip cookie; (a worthy quest, if there ever was one). Here is the post.

Why is the kitchen white? Is that 10 bags of flour? Have you stolen all that chocolate?! Where did these ovens come from?!! WHAT ARE YOU DOING WITH MY SPOON??!!

I'm trying to make the best cookies in the world.

Oh, ok. Carry on.

The author wanted to find a deterministic way to create cookies exactly the way he preferred them. In an attempt to do this, he launches into an impressively detailed workdown off all the essential ingredients, came up with reasonable dependencies, and was far more thorough about the details of creating the treat than I have ever seen in a kitchen related incident.

Normally I would have had a nice little chuckle, drooled a little at the sumptous pictures, felt sad about not having my own unlimited supply of cookies and moved on. But I remembered a discussion I was having with some of the blogmates a while ago, and then I asked this question.

Is this science?

The answer, of course, depends on your definition of science. 
Is this rigorous science? Hardly. There are too many variables, unmeasurable uncertainties, and a general lack of repitition.

But is this the kind of science that we want to encourage?

Quite definitely so. The first step to creating scientists and promoting scientific inquiry in general, is to start making people think like scientists. 
The way scientists assess the world, analyse information presented to them, and make decisions is a fundamentally better way to think than the usual flawed way that we approach problems.
This isn't anyone's fault. Human thinking does have its limitations, but allowing thoughts to be subject to scientific reasoning allows us to spot and weed out the errors and make better choices.

Cookie science?
Bring it on!

You Are What You Eat.

You are what you eat, as the maxim goes. But are you really?

Let's break this question up into two parts: What are you? and What do you eat?
So what is the shape of the human body? If you answered "Blob", no one would blame you. But the problem is, you're a blob, I'm a blob, Anne Hathaway is an extremely shapely blob; but how do we distinguish them? We can't. At least not scientifically. No one has any trouble distinguishing me from Anne Hathaway.

But, this is science; so we have to do things in a logical, orderly, reproducible way. 

Enter topology, the field of mathematics that deals with this kind of problem.
Here's what Wikipedia has to say about it:

Topology (from the Greek τόπος, "place", and λόγος, "study") is the mathematical study of shapes and topological spaces. It is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending.

Let's take a quick detour to look into topology a little more deeply and then using that knowledge, address our original question.
The most important aspect of topology is that it is not concerned with the exact shape or figure of the body, only the characteristic properties.
Let's look at some common shapes for examples.  Any three-dimensional body with no holes through it would be topologically equivalent to a sphere.  An ellipsoid is also a sphere, that is compressed from the sides. Remember that in topology, stretching and bending are allowed, and don't constitute a shape change. So topologically, a sphere is equivalent to an ellipsoid.

A sphere  (http://en.wikipedia.org/wiki/Sphere#Topology)

An ellipsoid (http://virtualmathmuseum.org/Surface/ellipsoid/ellipsoid.html)

Ok, but what does this have to do with the human body?
Well, the human body is three dimensional, but, it does have a hole through it. 
Wait, what?!
Yup, your digestive canal is actually a direct hole from your mouth to your, well, butt. 
That shape is defined as a toroid. Here's a picture of it.

A mesh diagram of a toroid.  (http://upload.wikimedia.org/wikipedia/commons/1/17/Torus.png)

Look familiar?
The toroid also has another casual name. We also refer to it as - the donut.

So bringing it all together, the human body has the same (topological) shape as a donut.
And that provides us with the solution to our question.

You are what you eat; if you eat a donut.

Now you recognise it. And your mouth is watering.  (http://en.wikipedia.org/wiki/File:Glazed-Donut.jpg)

Now that we know about topology, let's take it a bit further too.

Topology also allows continuous deformations. Here, you can pull and bend the solid (theoretically, of course) in ways that arn't physically possible (typical mathematicians).
Consider your coffee mug. Doesn't seem like a simple object to model, but when you consider it from a topological perspective, it is still a distinct shape.

A coffee mug is a donut too!   (http://en.wikipedia.org/wiki/Topology#Elementary_introduction)

Did you guess what is was?
If you bend it, stretch it, and push a little bit...

A coffee mug is a donut too!

So the next time someone asks you what you are drinking, you can honestly tell them it's coffee in a donut.

Further reading: 
http://en.wikipedia.org/wiki/Topology
http://mathworld.wolfram.com/Topology.html
 

Do you have any other interesting shapes that topologically form interesting things?
Let us know in the comments!