Small Distances Don't Mean Anything

Small distances don’t mean anything

Newton once famously said something that came to be known as his “flaming laser sword.” It came from a shared scientific belief that if something couldn’t be measured, it was useless to debate the nature of that thing.

Consider the classic question of an unstoppable force meeting an immovable object. The fact is that neither of the two can exist (which one begins to realize after taking a few physics courses). But even so, the question is ill formed, because it’s asking about things we can’t observe. At which point we are left with pure speculation as to what would happen.

We can only find out by setting up an experiment. Take an unstoppable force and an immovable object, place one in the path of the other and observe what happens. The object will either move or not, disproving the nature of one of the two.

But until we perform that experiment, it means nothing to speculate.

Here’s another consequence of this interesting worldview. Imagine the following, Heisenberg’s Uncertainty Principle is the following.

The uncertainty principle asserts a fundamental limit to the precision with which certain properties of a particle can be known simultaneously, such as position $x$ and momentum $p$. Where $h$ is Plank’s constant.

Imagine we wanted to know momentum, well that’s not terribly difficult right? Simply divide by the position.

However, what if we wanted to observe what happens at $10^{-35}$ m ? This is where things start to get interesting.

That shouldn’t be too hard, you might say. It’s just $Δx$ right?

Well, imagine what would happen. Because $E = pc$, we know that if we wanted to probe smaller and smaller distances, one way we could have that large of a momentum would be using photons with higher and higher energies.

The math lands us within the order of around $10^{19} GeV$. That’s a shitload of energy.

shit·load — /ˈSHitlōd/

noun, vulgar slang

a large amount or number.

“I have a shitload of work to do this week”

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  • David Awad
  • * Definition from Google

There’s actually an interesting consequence that happens here, because $E= m c^{2}$ we’ve got a bit of a problem. That energy can also be considered mass, for reasons that we won’t go into here. That’s a mass of about $ 10^{19} GeV / c^{2} $.

But if we compress this much mass to a space on the order of $1/10^{35}$ . . . it becomes a black hole. It's worth pointing out that a black hole is only called that because the escape velocity is larger than the speed of light, so we don’t actually know what happens inside of one because we can’t measure it. (this could change with the recent discovery of gravitational waves)

Well this is weird. If we have no way to measure what’s going on at such a small distance scale, now it doesn’t mean anything?

Well, according to some physicists. . . yeah.

This is an interesting consequence of what you might now realize is a bit of a Polarizing view. In fact, Adler goes on to say the same.

“While the Newtonian insistence on ensuring that any statement is testable by observation […] undoubtedly cuts out the crap, it also seems to cut out almost everything else as well”, as it prevents taking position on several topics such as politics or religion." 

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  • Michael Adler

This way of looking at the world, while undoubtedly clear, ends up being surprisingly narrow when it comes to problems that aren’t very well defined or well understood. Perhaps better described as human problems.

Post-Script:

Newton’s Flaming Laser Sword

The Uncertainty Principle

Why is mass equal to energy (a blog post all on it’s own)

The Discrete Expectation of Good

A probabilistic argument for nonreligious charitable works.

There is an assertion made by discrete mathematics, about the expected value of a given event. In its simplest form, mathematical expectation is the product of the amount a player stands to win and the probability that the player would win. In this short paper we will examine the meaning of the “expected value”, and use this property to make an assertion about the utility of different types of charitable deeds over a random sampling of people.

I’ll use the term “discrete” here as the following.

discrete: “individually separate and distinct.”

For example, a Dice roll is a very concrete example of an event with a discrete set of possibilities. As opposed to a doorknob which is continuous; it has states of locked and unlocked, however it rotates, between them, has values in between the two states.

“oh, cool” You say to me, “But isn’t this is an argument about charity?” Well that will become clear in a bit.

We’ll start with a ‘dice-roll’ to give you an idea of what I mean.

A typical die, has 6 sides, with dots clearly denoting which value has been selected randomly by the die roll.

There are 6 possible outcomes of rolling a die, each clearly defined and equally likely.

A die has to land on one of the sides, with a particular side facing up. That side being the corresponding value to that dice roll. This may seem a bit like we’re being pedantic, and we are; but we’ll see how this becomes relevant when we get to charitable deeds.

So what is the Expectation of a dice roll? Well, Expectation is defined as the sum of each possible value, times by the corresponding probability for each of those values. Each value on the dice is equally likely, so we end of with the following:

Each outcome is equally likely when rolling dice, so there’s a $\frac{1}{6}$ chance of any of the values.

let’s call the outcome of our dice $d$ instead just for convenience

simplifying that out we get

“Okay cool,” you say again, “but what does this math mumbo jumbo have to do with religious charity?”

Let’s imagine applying this reasoning of expectation and probability applied to charitable works that you can do. Before we can do that however; It is important to more concretely define the concept of what good is.

Good: that which is morally right; righteousness.

Me: Sure, but there’s also a sort of goodwill or karma that some associate as the outcome or benefit of doing something “good” for someone else. That, whatever you determine it to be; will be what I am referring to as “good” in the context of this argument.


Well, when you perform a charitable deed such as say go on a religious visitation, or visit foreign countries to build churches. There is a chance that a person may not receive the same amount of “good” that you intend to give.

This could quite literally be because they just don’t believe the same thing that you do. The fact is that not all people believe the same things. If they don’t share the beliefs that inspire your deeds, they probably won’t appreciate religiously motivated works of charity.

“As of 2010, Christianity was by far the world’s largest religion, with an estimated 2.2 billion adherents, nearly a third (31 percent) of all 6.9 billion people on Earth,” the Pew report says. “Islam was second, with 1.6 billion adherents, or 23 percent of the global population.” — NPR

Let’s abstract this away, round up, and assert that say, $\frac{1}{3}$ of humanity is christian. (It doesn’t really matter what religion it is, because all that matters is that there are people who believe different ones)

So let’s imagine a “good class”, which is the set of all deeds which you can do (religious and non-religious) that are received as an equal amount of good. (in the case of religious deeds, this would be deeds done for same believers)

Looking at the nonreligious deeds.

Let’s look at an expectation of the possible good you can do for whoever could receive these deeds. If we’re looking at nonreligious acts of good; the expectation is something like the following. We’ll use one ‘$g$’ to denote a unit of good (whatever that is). And so everything in our good class is worth 1g. We’ll look at the probability that that individual will interpret that event as a good deed.

The probability of something being good is 1 in this case, because there’s nothing religious about whatever good deeds we’re concerned with.

For example I think most people agree that giving food to the homeless would probably be a better charitable deed than giving them bibles.

Now let’s look at the religious case

The probability of a religious deed such as building a church, is not likely to be uniformly interpreted as good, it’s “goodness” is contingent upon the recipient of the deed.

So if we consider $P(“good”)$ to be contingent upon the recipient, then we arrive at only a $\frac{1}{3}$ probability that the recipient is a christian that would receive that same amount of good.

Substituting in $P(“good”) = \frac{1}{3}$ we get:

If in general it is more likely that our non religious charitable acts will be interpreted as good because they don’t have religious associations.

quod erat demonstrandum

Thanks for reading!

P.S. You could argue I’m doing a bit of informal ‘hand-waving’ here when it comes to addressing the issue of a good deed being morally equivalent to another. For those of you who are so inclined, this argument still holds if you believe there exists any two or more religious and nonreligious deeds that are of equal “good” value. Because if that is the case, then nonreligious deeds will always yield a higher expectation of “good” over the course of a lifetime.

As long as you apply a consistent definition of “good” throughout this short blog post, i think the argument holds.

Sources:

German Beekeeping Law

and the hilarity that ensues…

If you’re like me and have been reading the German civil code for fun in what little spare time you have, check out Section 3, subsection 960. You’ll notice some interesting legislation on the subject of ownership.

There may be some entertainment to be found by shedding some light on legislation regarding wild animals, and specifically the ownership of a swarm of bees.

Let’s start with the definition.

Swarm: a large or dense group of insects, especially flying ones.

Now let’s look at how the German Civil Code deals with situations involving densely packed groups of bees.

My swarm of bees is flying away! What do I do?

Well, it would seem that your only option is to chase after them.


Loss of ownership of bee swarms:

Where a swarm of bees takes flight, it becomes ownerless if the owner fails to pursue it without undue delay or if he gives up the pursuit.

— German Civil Code § 960–61

Wait… So If my bees fly away apparently I have to chase after them, or else they’re not mine anymore and are considered wild animals per subsection 96o. I suppose that makes some sense.

But pursuing them … what does that mean exactly? What if they fly into someone’s house? You can’t follow them can you?

Wait, it just flew into my neighbors empty beehive! Those are my bees in there I’m sure of it!

Well, my friend the german civil code has you covered.


Right of pursuit of the owner:

The owner of the swarm of bees may, in pursuit, enter on plots of land belonging to others. If the swarm has entered an unoccupied beehive belonging to another, the owner of the swarm, for the purpose of capturing it, may open the hive and remove or break out the combs. He must make compensation for the damage caused.

— German Civil Code § 962

So as long as you are legally in pursuit of your swarm of bees, you are considered to be the owner, and can invade other people’s property, and even destroy it. As long as it’s for the bees and you pay up later.

Hey wait a second, I think there were already bees in this beehive that mine flew into…

The German Civil Code handles this as well! Telling you that you’re basically out of luck. If your bees fly into someone else’s swarm; you’re basically screwed.


Intermixture of bee swarms:

If a bee swarm has moved into an occupied beehive belonging to another, the ownership and the other rights in the bees that were occupying the beehive extend to the swarm that has moved in. The ownership and the other rights in the swarm that has moved in are extinguished.

— German Civil Code § 964.

The thing that really strikes me is the sequence of events that must of occurred in order for this series of laws to have even been established. And it only gets better! The civil code goes on to list a statute for what happens when different swarms of bees have merged together.

At some point; someone had to have said, “Hey look! Those are my bees over there! Flying toward that other swarm of bees that someone else is chasing! Are you kidding me?!” And I guess this must have happened a lot because we now get to this.


Merging of bee swarms:

If bee swarms of more than one owner that have moved out merge, the owners who have pursued their swarms become co-owners of the total swarm captured; the shares are determined according to the number of swarms pursued.

— German Civil Code § 963

Even if you owned the majority of the swarm it doesn’t matter.

Deutschland sagt, “saugt den Imker soundrel saugen!”

Let’s imagine a hypothetical here. Ten swarms are flying around one particularly unfortunate neighborhood, followed by an army of 5 bee­keepers flailing around with pitchforks, butterfly nets, torches, and katana swords destroying everything in their path(legally of course).

Two of them rightfully owning their respective swarms, another chasing after two different swarms that happened to escape from him, and a third who hasn’t lost any bees but happens to like running in mobs. etc.

What happens if they happen to merge together into separate, but larger swarms? Or what if gasp they all combine together to form the überSchwärm?

Well… I don’t want to be the guy stuck counting out a swarm of bees 10 ways; I’ll say that.

Sources :

  • The German Civil Code

  • Also a quick shout out to Shy Ruparel and Sam Agnew who originally mentioned German Beekeeping law as an attempt to entertain the crowd.

Game Theory, Banana Theft, and Why It's Always Better to Betray Friends if You Get Caught.

Have you ever looked into Game Theory? If not, you should. It’s pretty interesting.

Game Theory: The branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants. Game theory has been applied to contexts in war, business, and biology.

  • google.com definition

So basically the math behind making the smartest possible decisions in any game, or decision process. You might be thinking, “well, after all those horrible SAT word problems I’m never going to be able to use any of this math mumbo-jumbo.” You’d be surprised what kinds of implications game theory can have on how we can make decisions. It’s all about keeping track of all of the possibilities.

Imagine the following scenario, you and your best friend have committed some heinous crime; just off the top of my head let’s go with the theft of a banana.

You've snuck into a walmart and fiendishly made off with one of the prized fallic fruits. The fuzz is unto you though. They track you down after finding a set of fake passports hidden in a safe behind a slew of one direction posters in your bedroom. They trace you to Aruba where you’ve escaped for your early retirement with the money from the banana heist.

You’ve now been extradited back to America for questioning. Putting each of you in separate rooms; with no means of communicating with your colleague to collude on how to conceal your clandestine caper. The prosecutors are sure that one of you have committed the crime. But they don’t have the evidence to prove it since you’ve stealthily hidden the pilfered plantain. (yes, I’m going to keep my thesaurus open for the duration of the narrative.) So they can’t get you on banana theft, a criminal charge punishable by a minimum of 3 years in jail. They can only really get you on banana misconduct, a much lesser charge facing up to 2 years.

Since they don’t have proper evidence to convict either of you of the theft; They hope to get you both sentenced to a year in prison on the lesser charge. The prosecutors offer both of you an out: betray the other by testifying that the other pocketed the produce, or to cooperate with the other by remaining silent. The possibilities are the following for you and your friend, (we’ll just use A & B for convenience, respectively.)

  • If A and B each betray the other, each of them serves 2 years in prison.
  • If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison. (and vice versa)
  • If A and B both remain silent, both of them will only serve 1 year in prison. (on the lesser charge)
Well this is an interesting problem, If you don’t know what your friend is going to choose, you could end up screwing them if they end up backing staying silent and you don’t. But if you stay silent the same thing could happen to you. So what do you do? Stay silent or rat them out? #### Here’s where game theory comes in. Game theory introduces the idea of measuring decisions by using **utility**.

Utility: An economic agent is, by definition, an entity with preferences. Game theorists, like economists and philosophers studying rational decision-making, describe these by means of an abstract concept called utility.

  • google.com definition

The utility of betraying them is in fact higher, despite collaboration being the better option for the two of you.

Here’s why, Let’s imagine this from the standpoint of A, yourself. Regardless of what your friend B decides right now, we know that they’re going to choose. Just like you, B can choose to stay silent, or betray you.

  • If B cooperates, you should defect, because going free is better than serving 1 year in prison with banana haters.

  • If B betrays you, you should also defect, because serving 2 years is better than serving 3.

So either way, A should defect. Parallel reasoning will show that B should also defect based on what you might do.

“The utility of betrayal is de facto higher, when it is considered from the standpoint of the individual”

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  • David Awad

if we’re being pedantic, we’ve used a little bit of a narrow definition for rationality here because we’ve assumed that you and your friend have no loyalty to each other whatsoever, and also that you don’t consider any negative outcomes from betraying each other afterwards. But I think I’ve gotten my point across.

There are a lot of other interesting consequences that come from critically analyzing possible decisions in games, and this is a rather contrived and dare I say, fruity example. It’s really interesting to critically examine games and other decisions we make in life if we assume that the other players are playing optimally, and how we should decide based on that.

So no matter what you’re going to jail it seems… I guess stealing that banana had pretty… low utility.

Sources:

What makes you... you?

You’re probably not who you think you are…

A philosophical inspection of the notion of personal identity

So what is a personal identity? What is it that makes you who you are?

There are a couple ways to go about defining this initially rather abstract and humanly invented concept. You first must decide what it is that determines who you are. Is it you? Well it would have to be, although your parents do decide the most crucial part of your identity, which is your name.

Hrmm…

Well, let’s look at it from a more literal perspective. I am a person, with a body, and a “mind” that is resultant from the functions of my brain and my subconscious. But let’s abstract the neuroscience from the matter and simply say, that a person consists of the contents of your brain, which I will colloquially refer to as the mind, and a body. A person consists of a mind and body.

What is it for each of us to exist? Which properties, if I lost them, would mean I would no longer be what I am?

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  • René Descartes

We’re working with a definition of a person as a combination of your body and your mind. So which is essential to the notion of personal identity? Is it your brain or your body that determines who you are?

Let’s examine both ideas, and see what we end up with.

If it were in fact the physical body that determined who you are… what would this mean?

On the body…

Let’s look at a slightly contrived example, let’s look at the hypothetical Amy and Brian. Both have bodies, and both have minds. What if we switched their minds? Who is who? Well, Amy now has Brian’s mind, and all the thoughts and ideas of Brian. Brian also has Amy’s mind, and so we would consider them now to be each other? Certainly most of the people they know might not notice the difference until after talking for a little while.

More interestingly, what if we cloned someone.

But this is a bit of a contrived example and doesn’t happen in the real world.

Which brings us to things like accidents, or, more generally changes to the physical body. What happens when people’s bodies change? We define Sarah to be Sarah at any given time based solely on the fact that Sarah’s body is there. But what if Sarah experiences some tragic accident and no longer has an arm, or becomes handicapped in some other way? The body has changed, but has the person changed? Frank isn’t somehow not Frank just because he broke his leg.

This must mean that it is the mind that actually determines what someone’s personal identity is, and this is certainly the more intuitive viewpoint, however there are some problems that come with this viewpoint as well.

On the mind…

Imagine then, the very simple example. Derek is who he is, because of the contents of his mind right now.

What about tomorrow, what if his opinion changes, or he learns something. And there are still of course the accidents that affect the brain that result in a very changed personality. Do people with slightly changed brains or ideas have the same exact mind? Probably not. In which case that would mean they are by definition not the same person. But we certainly don’t do that. On the day to day we still refer to each other as the same people.

There’s yet another problem that also arises. What if you were able to create a computer, (and this technology exists) that could perfectly replicate a person’s reactions to certain stimuli and ideas? This computer could effectively recreate the mind of a person. Surely the computer is faster, but what would that mean for our person? Which entity is more you?

Modern philosophers actually refer to things like names as a convenient illusion for personal identity. Because the concept itself is actually incoherent. These complex problems have resulted in a very interesting modern definition for what personal identity actually is.

Personal Identity: the persistent and continuous unity of the individual person normally attested by continuity of memory with present consciousness.

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  • Google

Post-Script

If you’re interested in further reading on the nature of personal identity in philosophy, try checking out Stanford’s dictionary of philosophy on the subject.

There is also an absolutely fantastic paper on this entitled, “Where am I” by Modern Philosopher Daniel Dennet on the notion of personal identity.