Spherical Pony Life · 9:03pm Nov 23rd, 2020
There are many old jokes about physicists and spherical animals. Cows are a favourite, but other species, including ponies, also feature. Here is one example (taken from this source):
A geneticist, a physiologist and a physicist were summoned to meet a wealthy racehorse magnate. He told them he would give a million pounds to the one who could accurately identify race-winning horses. After six months of hard work, they returned to present their results to the expectant millionaire.
The geneticist said, "I've looked into all the current genetic research, checked blood-lines going back decades, but there are just too many behavioural and environmental factors. I can't help."
The physiologist said, "I've looked at muscle mass, bone volume and density, and all the other factors I can think of, but the problem's too complex. There's just no guarantee of predicting a winner."
Finally, the physicist calmly walks up to the millionaire and gives him an index card. "Here you go," he says "I've found an equation that solves the problem for you."
"Wow," said the millionaire, "That's impressive…I'll get my cheque book."
"Great. But there's one thing you should know," said the physicist. "It only works for a spherically symmetric horse travelling in a vacuum."
The idea is to ridicule the simplifications made by theoretical physicists. Such spherical assumptions rarely make effective ways to study zoology, understand horses, or solve friendship problems.
However, any theoretical physicist will gladly give examples of things you can learn from this approach, and explain how by ignoring the irrelevant details, you can focus on the important science. This is how they think. If you want to understand the Universe, you can’t get too hung up about the shape of individual galaxies, or the details of an insignificant blue-green planet orbiting an unregarded yellow sun.
One thing you can show by considering spherical animals is a fundamental principle of biological scaling. The volume of a spherical critter scales with its radius cubed: \frac{4}{3}\pi r^3, while its surface area scales as the radius squared: 4\pi r^2. Thus, the surface area you get for a small sphere is a lot bigger, relate to the volume, than for a large globe. Hence a tiny bacterium can get all the nutrients it needs from the environment by just letting them diffuse through its membrane, while large animals need much more sophisticated respiratory systems, and have to actively hunt for food.
This scaling is law also tells us that you can’t just make a big animal by scaling up a smaller one.
Make a pony 10 times taller and her volume increases by 1000. If the density of pony stays the same, that means she is 1000 times heavier, but the surface area of her neck is only 100 times larger. So, without an effective strengthening spell, her head will fall off. Although breeders have produced horses ranging in height from miniatures under 0.9m to Clydesdales over 1.8m, we should not expect selective breeding to produce even bigger giants as there is a fundamental limit.
Very large animals have smaller heads relative to their body size, unless they spend all the time in water like whales and dolphins, so their necks can support the weight. Yet if we look at the ponies of Equestria, they have an abnormally large head to body size ratio. This distortion has been pushed further in Pony Life, driven by different scaling laws that correlate the relative head size to cuteness. As they don’t have feather-weight brains, then we should consider that they either have magically reinforced spinal cords, or perhaps we should conclude that Equestria operates on a different scale and these are indeed little ponies.
I remember one example given at the start of the semester was the cooking time of a turkey, assuming a spherical turkey. The cool thing was that by some unit-canceling trickery we got an exponential factor describing the relation between turkey weight and cook time that was supposedly independent of the bird’s shape. I didn’t get a chance to test the formula empirically though
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I remain convinced that that universe was created by Pinkie while she had all of Discord's power. Its physical laws only vaguely resemble our own, and taste far better.
Given the amount of damage they don't take from falls and having pony-sized objects dropped on them, they're probably the size of mice!
Trouble is, you then get people who then try and simplify to a zero point with mass?
5403754
Sounds like there might be some circular reasoning going on there.
5403758
So if there is a Pony Life episode where Pinkie Pie acquires all Discord's power, what flavour of new universe would that spawn?
5403772
Or made of plastic.
5403784
For theoretical physicists, there is a balance to be reached, where it is sufficiently challenging to keep them interested, but not so complicated that they get fed up before they finish the calculation.
5403816
Strange and charming from top to bottom. Also cherry.
You're missing a phrase from the joke:
First, assume a spherical horse of uniform density....
5403816
Assume a spherical joke of uniform mirth in a conversational vacuum
5403816
I wish I could remember seeing the thing I was trying to remember. A 3D representation of Amplitude, Frequency and Time?, where the Frequency/Amplitude went from a pure sine to a single line, at the point where the Time? went from a flat constant amplitude to a point? giving the two extremes of pure tone to pure white noise? The important bit was the mid point, where the two axis ended up with Gaussian distributions, which total area/volume was 16*Pi, The Heisenburg Uncertainty limit?
The Image, animation is a Lot easier to watch than describe.
5403846
But can a chimera, bombinating in a vacuum, devour second intentions?
5404120
Only as the period approaches the end of this sentence.
People forget how little they matter all the time.
(No, this is the intended Twilight emoji. Go look up how nihilism actually works instead of how fiction uses it)
5403772
Or, say, the size of MLP toys? I've seen fics to that effect...
5404259
Yeah, I'm thinking the blindbags are just about right. The plastic is pretty tough, too!
5403758
I like to think that Pony Life is a series of bedtime stories that EQG Pinkie tells Little Cheese in the future. It's why everyone has smart phones and tablets.
5404392
That... that's adorable
That is inelegant. interior is (d-1)/d)τr^d for interior. For the interface with its space, we use:
(d-1)τr^(d-1)
The equation for interior of a circle is ½tr^2. The perimeter of a circle is τr. If we bump it up a dimension to 3D, we have ⅔τr^3 for volume and 2τr^2 for area. Choosing the right constant make the mathematics easier. Indeed, many people see πr^2 for area of a circle and believe that πr^3 must be the volume of a sphere. I wonder how many engineering disasters this has caused. If only people would use the correct constants, we could avoid such errors.
5405830
I was waiting for you to post something about this. Good to know you're well.
5405884
Using Tau makes the mathematics easier and more elegant. It avoids the mistake of"Area is 'πr^2=a'; so therefore, 'πr^3=v" is volume." because one learns that the 1st equation has an hidden cancellation of 2 and the general equation is "(d-1)/dτr^d=interior".
The 23rds was the anniversary of getting runover. I need to write a BlogPost about that and almost getting runover again.
Oh, I should probably chip in that frictionless vacuums are another favorite of theoretical physicists and jokes thereof, at least until some psychopath traps them in one. (The alt-text mentions an infinite plane of uniform density, yet another abstraction)
5403819
What about up and down?
5520502
Way too low-energy for Pony Life.
5520518
I think I get it because up and down quarks are low energy particles and create stable matter, while the other quarks create unstable matter.
5403758
Does have big Ponkers energy to it. I've only seen like 5 episodes I need to watch the rest the next time I drop acid.