Lucky the Physics Wizard by KimB

Lucky is one lucky cat! Actually, he's lucky to be alive, lucky to have a home, lucky to have food and fresh water delivered directly to his bowls twice daily, by humans rather than by drone-drop. Lucky is coming 3 years old and is the quintessential "curious cat". He loves to explore and is an extreme cat-acrobat, finding his way to the top of bookcases and balcony perches to observe the activities of his human-pets.

Lucky also likes to "play ball".

I've only had one dog that liked to retrieve or "play ball", all the other dogs were far too smart to be enticed from their comfy positions on the couch, to run around chasing an object only to find that it gets hurled away again. Their attitude was: If you didn't want it, why did you ask me to go get it for you?

But Lucky the cat, loves to "play ball".

In and amongst the many cat toys purchased and normally completely ignored by the other cats (Othello and Bette), are small yellow tennis balls. I don't suppose the color means anything to Lucky but the fuzzy outside let him carry it around. Like most dull-minded humans, we expected Lucky to "entertain himself" with the toy: sort of like a parent's smartphone equivalent to not having to bother with their children in any meaningful way: Here take it, now leave us alone. Lucky did the common thing with the ball, bat it around, chase it a bit and when bored got back up on the bannister to watch the never ending chaos of human's doing purposeful activities like: sweeping up the tracked cat litter from the no-track-cat-litter that tracks anyway.



Lucky
The surveillance cat

Then Lucky found a new thing to do with the yellow ball. He brought it to me and dropped at my feet. It was rather like a cat present of a dead mouse, except Lucky is indoors and thankfully we don't have many mice, and it was a small tennis ball instead of a dead mouse. I thanked him and gave him a pat on the head and picked up the ball. Then I tossed causally it towards the pile of the other ignored cat toys. Lucky went ECSTATIC!

He raced to the ball, gave it a few perfunctory bats, picked it up and brought it to me, dropping it at my feet. When I tossed it again, thinking this was a one-off behavior, Lucky raced after the ball and brought it to me again and again and again. Lucky discovered the game of ball and was delighted that his normally dull minded humans, had learned something - at last!

Lucky found a more fun way to play ball when he insisted on me tossing the ball up the stairs so he could race up the stairs to get it. Actually it took him a few tries to get me to move to the stairs. First he dropped the ball just out of reach and if I didn't move to pick it up he lightly batted it towards me until I picked it up and he raced towards base of the stairs waiting for the toss. Finally, I got the message: he wanted me to toss the ball to the top of the stairs.

Pretty much anyone who has a cat has watched them play solo-soccer with a toy. They have such eye-paw dexterity that I'm sure human soccer players are hoping for a DNA transplant of cat-soccer-genes so they can do something half-way the same. They bat the toy here and there for a few minutes then head for the warm sunny spots to sleep off their embarrassment of actually having moved at all. Normally, I just smile and enjoy the show for as long as it lasts but never spent too much time thinking about it.

Animals are not stupid. They think differently than people and they certainly have completely different goals than we do. Animals seldom worry too much about anything, especially when they can see their food dishes are filled and they know that fresh water is in the bowl. And generally that's about all humans pay attention to too. However, people that work with or train animals of all kinds, know there is something else going on inside their skulls. Each animal and each species, like individual humans, has a hierarchy of priorities and behaviors that go with them. Cats are not particularly high on the list for training, but they have their own intelligence levels.

Nearly everyone has seen those Wild Lion documentaries where the lionesses surround a group of zebra and then on some unspoken signal rush the herd, like it's Super Bowl Sunday with 30 seconds left on the clock. They triangulate on a target, fake left-right and race up the center towards their goal. We've also seen the videos where some of the rookie lionesses jump off-side and everyone goes home with a no dinner for you tonight penalty.

They do some pretty intense calculations, the kind that takes some gnarly mathematics to explain but the kind that humans can do in a nanosecond. We have to teach our children not to cross the road without looking for cars (soon to be driverless empty cars going nowhere in particular because there is no one in them) but after a while they can calculate: Can I get across the street before the car gets to this point?

Humans and lions can calculate the velocity¹ of an object, which is the rate of change in its position with respect to a frame of reference, and is a function of time. ²

• How fast can I move
• How fast is the car/zebra moving
• What direction is it going
• Is it going to change direction
• Is it going to speed up/slow down
• Is there anything that can interfere like a stop sign or a stream
• How long will it take to get from here to there

Like the lionesses, if we think we can get to the other side safely, then we cross the street/race towards the zebra. Unfortunately for a lot of animals they have no frame of reference for cars, trucks and drones and we see the results as road kill. Humans outside of a driverless-car may not have a frame of reference either; now we have to add in: it is there a human driving or a computer? It may not be certain that the car "will" slow down but our experience shows human drivers "may" slow down. Computers are supposed to slow down but if they don't, you pay the same penalty as the ground squirrel crushed on the roadway. If you see a human holding a phone while driving you might change your mind about crossing the street; there is no way to know what the computer driving the car is doing: it is processing or noticing you or is it steaming a Netflix or getting an over-the-air real-time update that temporarily interrupts it's "view of you"?

Kinematics
mass m, position r, velocity v, acceleration a

Animals also have a sense about "The World". They know direction and up from down. A long time ago, I watched a documentary about different ways researchers were testing animal perceptions. The researcher had some small monkeys called tamarins ³ (exceptionally and fatally cute). He set up a large clear box with 3 black tubes on the outside leading to matching food bins on the inside. The monkey could not see that the researcher could change the pathway of the tubes, from the monkey's view: each tube lead directly to a food bin. The researcher showed the monkey the food item and dropped it into one of the 3 tubes. The monkey went to the food bin directly under each tube to get the food. Then the researcher changed the pathway and again showed the monkey that the food was going in tube 1 but it came out at food bin 3. The monkey stared and stared because even monkeys don't believe in magic. The monkey knew that things Fall Down, they don't Fall Sideways.

So, animals have a sense of the world and how gravity ⁴ works. Bananas don't Fall Sideways and they don't Fall Up. It was Isaac Newton ⁵ in 1687 that explained this to humans. ⁶

I admired Lucky's ability to race up the stairs over and over and play pounce at the top to get the ball. Lucky is sleek and quick and has the longest tail ever on a cat. Watching Lucky bounding up the stairs was like watching a lioness trying for a solo kill on a zebra. I didn't pay much attention when he carried the ball down the stairs to me and waited for the next toss. It's what dogs do when they play fetch and I just lumped Lucky in with dogs but of course, Lucky is a cat not a dog. What is even more remarkable is that whenever he wants to play ball, he brings a ball that he has hidden and sits with it at my feet patiently waiting for me to pay attention.

Then I noticed a slight shift in his play. He didn't want to lose his advantage of being on the middle step by coming all the way to the bottom so he dropped the ball midway and let it roll down the steps to me. OK, I will admit to being not too bright about what he was doing and it took a longish while for me to see that after he dropped the ball it always came directly to me.

That's right. It came directly to me.

It didn't matter where on the stairs he dropped it. It didn't matter if he dropped it more left than right or up one or down one from where he sat. He would give a push with his paw and it would bounce down the stairs where I could just pick it up. Once I began to notice I could see he did other things too to get the ball to me: he could bank it left or right against the walls lining the stair. He could double bank it. He could put spin ⁷ on it. He could combine spins: top and side and bank the ball at the same time. He used just enough force ⁸ on the ball so that as it bounced down the stairs it would lose velocity and come to rest in front of me. Occasionally, he would take a big whack and I would think "Oh, he's lost it..." only to realize he was hitting the wall behind me and ricocheting ⁹ the ball off the back wall towards me.

Of course, sometimes he does miss, but I think it's more that he doesn't want me to get bored and if he makes me move all of 6 inches to reach the ball then I will continue to play until HE gets tired.

Now as I watch Lucky play ball, racing up the stairs, making his pounce and then dropping the ball and pushing it in such a way as it reaches me, I think of all the things Lucky must be calculating . Things that even the smartest humans work hard to understand.

1. Physics ¹⁰ the 'knowledge of nature', is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental scientific disciplines, the main goal of physics is to understand how the universe behaves.
   The world around us and how it works.
2. Classical mechanics ¹¹ , also known as Newtonian mechanics ¹¹ is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces.
   What goes up, comes down. Why things move and why they stop.
3. Dynamical system ¹² / Dynamical billiards ¹² in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. Billiard dynamical systems are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional.
   How banks, topspin, backspin work.
4. non-Euclidean geometry ¹³ when parallel lines drawn on a curved surface do not remain equal distant.
   Like cutting segments from an orange or drawing lines on a ball or decorations on a bowl or jug.
5. Outer billiards ¹⁴ is a dynamical system based on a convex shape in the plane. Outer billiards differs from a usual dynamical billiard in that it deals with a discrete sequence of moves outside the shape rather than inside of it.
   Like bumper pool which has obstacles in the middle of the table.¹⁵

The Bunimovich stadium
a chaotic dynamical billiard

Lucky with his happy-go-lucky personality, his grey coat and his extra long tail is one very smart cat.

Lucky
contemplating the universe

References

1. https://en.wikipedia.org/wiki/Velocity
2. https://en.wikipedia.org/wiki/Kinematics
3. https://en.wikipedia.org/wiki/Tamarin
4. https://en.wikipedia.org/wiki/Gravity
5. https://en.wikipedia.org/wiki/Isaac_Newton
6. https://en.wikipedia.org/wiki/Gravity#Newton's_theory_of_gravitation
7. https://en.wikipedia.org/wiki/Magnus_effect
8. https://en.wikipedia.org/wiki/Force
9. https://en.wikipedia.org/wiki/Ricochet
10. https://en.wikipedia.org/wiki/Physics
11. a) https://en.wikipedia.org/wiki/Newtonian_mechanics
    b) https://en.wikipedia.org/wiki/Classical_mechanics
12. a) https://en.wikipedia.org/wiki/Dynamical_system
    b) https://en.wikipedia.org/wiki/Dynamical_billiards
13. https://en.wikipedia.org/wiki/Non-Euclidean_geometry
14. https://en.wikipedia.org/wiki/Outer_billiard
15. https://en.wikipedia.org/wiki/Bumper_pool