Is this Post Anti-Semitic?

First off, I hope the answer is no. According to my understanding of antisemitism, nothing I have ever written would qualify as being anti-Semitic. But my understanding is not the only one. There are many people who might deem a lot of my criticisms of Judaism and Jewish practices as anti-Semitic.

Before I get into the meat of the post, I'll note that antisemitism is real and appears to be on the rise. The Anti-Defamation League (ADL) notes that in 2017, anti-Semitic events increased by 50% over 2016 and more than doubled since 2015. I have no reason to dispute these numbers. ADL breaks down anti-Semitic incidents between harassment, vandalism and assault, of which the first two are dominant and about equally split. Vandalism, for example, is often a very clear cut example of anti-Semitic behavior. But there are many other behaviors that aren't so clear cut. It turns out that there are lots of people who have a vested interest in muddying the waters of what is or isn't antisemitism. Let's look at these parties.

Why Racists Muddy the Waters

The first group who regularly muddies the waters are the racists and bigots, namely the anti-Semites themselves. There are lots of ways in which they operate. One obvious one is to disguise anti-Semitic statements in more banal terms. This is sometimes referred to as dog-whistling. The idea here is that other anti-Semites pick up on the terminology and recognize the speaker as one of their own. However, because the term is "hidden," they maintain plausible deniability for the rest of the population. One example of dog-whistling is the use of a term like "globalists." An anti-Semite can say this and other anti-Semites hear "Jews" while the rest of the population might hear "someone who supports international agreements at the expense of national sovereignty." People have caught onto this word, but they'll just keep on coming up with more and more dog whistles.

Another way anti-Semites benefit from muddying the waters is that they are able to expand what is considered legitimate critiques. By constantly pushing the boundaries of what is acceptable they may eventually broaden that region of acceptability. This tactic was used to great affect by Nazi Germany among others.

Here's yet another insidious way that anti-Semites use gray areas to their own benefits. Let's say you are someone who would like all Jews to leave your country. You can't just say that, at least you can't in most places. But what you can do is start agitating for things like banning ritual slaughter or circumcision. The basic idea here is that you co-opt an issue for your own anti-Semitic purposes. You get to dodge criticisms of antisemitism because you can always say that you are supporting animal rights or children's' rights. And it just so happens that there already are a lot of people who are not anti-Semitic who oppose ritual slaughter and circumcision that you can point to and essentially hide behind.

Why Religious Zealots Muddy the Waters

The other group that likes to muddy the waters is religious zealots. Let's use circumcision again as an example. There are a lot of reasons that we as a society should have a debate on whether we should be circumcising infants. However, if you are a religious Jew this is not a good debate for you to have. It's far better to dismiss it as mere bigotry. The more things you can sweep away as anti-Semitic the less you actually have to play defense. If you can claim every religious critique is anti-Semitic you never need to justify anything.

I've encountered this approach many times among religious Jews regarding biblical criticism. They will say that Wellhausen, one of the original biblical critics, was an anti-Semite therefore all of biblical criticism is an exercise in antisemitism. This is a pretty hollow attack, but it sets up a nice wall that other religious people can hide behind in order to not have to engage with the various assaults that biblical criticism mounts against traditional interpretations. The end result of all this if the religious adherent manages to broaden the definition of antisemitism to include things that aren't really anti-Semitic, then they can safely inoculate themselves and their communities against any critique that arises from that gray area. They just claim it's all antisemitically motivated and move on.

All these muddy areas make it very difficult to navigate as someone who has opinions on various features of Jewish ideology. It's probably true that anti-Semites can find stuff I write and use it on their own. After all, I have written some pretty strong criticisms of various parts of the Hebrew Bible and the Talmud. Yet by not voicing my criticisms because of fears of being labeled anti-Semitic, I'm letting both the anti-Semites and the religious zealots win. 

Nowhere is this muddy area more difficult to navigate than with regard to the state of Israel. So let's dive headfirst into this treacherous land.

Israel is a Huge Muddy Morass

When I transitioned from a religious Jew to an atheist it allowed me to take a less dogmatic view towards Israel. The religious view is that the land of Israel from the Mediterranean to the Jordan (and even a bit beyond) was granted to the Jews by divine right. Once I no longer believe that, and later found that large portions of that area where never controlled by any Jewish entity, things started getting very gray very quickly. Yet, I found the whole topic extremely difficult to get good information on.

Both sides, the anti-Semites and the religious zealots benefit from criticisms of Israel being viewed entirely in anti-Semitic black-white terms. As such, I've probably encountered more propaganda with regard to Israel than I have in almost any other issue I've tried to research. Anti-Semites use it as a way to inject some of their hatred into mainstream topics, and the religious use it to deflect any critiques. Is there a way forward to how we can possibly separate discussions about Israel from the giant anti-Semitic rhetorical swamp that surrounds it?

Natan Sharansky tried to do this. He created the 3 "D" test for whether a critique of Israel is legitimate or not. His 3 Ds are:

1. Deligitimization: referring to Israel as not a legitimate state capable of self-determination
2. Demonization: referring to groups as evil or demonic
3. Double Standards: criticizing Israel on certain issues while ignoring worse issues elsewhere

Any critique of Israel that uses one of those "D"s, according to Sharansky, is grounded in antisemitism. I agree with Sharansky about the second of those Ds. To me that seems pretty clear. But the first and the third deserve some more thought. As of now, I'm not sure whether I agree with Sharansky or not.  This is one of the things that I plan to think and write about over the next month or so. I'm not sure when the next post will be (I have some trips coming up and a change of residence). My current plan though is to tackle D1 and D3.

More ways not to know, chaos, quantum physics, and even more bizarre

Previously, we discussed some of the ways you might not know something. I pointed out that religious thinking deals in absolute certainty of knowing, while science always allows for uncertainty. We looked mainly at statistical uncertainties in the previous post, but there are even more fundamental uncertainties in the universe.

A Very Brief Primer on Chaos Theory

Perhaps you might have heard of the "butterfly effect" which, in the original formulation, is the idea that a butterfly can flap its wings in Brazil and cause a tornado in Texas. Personally I find this a more confusing than helpful representation of what we'll term "chaotic behavior." But it's what you may be familiar with so by the end of this section hopefully you'll understand what is actually meant by this.


The basic idea of chaos theory is that there are some systems where small differences in their initial conditions can eventually dominate the behavior of the system. Let's look at a very simple example, the Logistic Map. The logistic map is governed by a very simple function. Start with a value x₀ between 0 and 1, and then choose another value r. Now compute the value r (x₀)(1 - x₀) and call this x₁. Now repeat this process with  x₁ in place of x₀ to get x₂. And so on and so on.  In this system it's convenient to consider what these terms could mean.  A common interpretation is that this equation models the population of a species. Each time you run the equation, say to produce x₁, you compute a new population, and the result is based on the population of the preceding generation, in this case x₀ and the constant r.

What happens when you calculate the population after many iterations?  Well it all depends on what you choose for r. If you choose r between 0 and 1, you originally will get to 0, regardless of what value of x₀ you start with. If you choose r between 1 and 3, the population will eventually stabilize at some value. It doesn't matter what we start with we always end in the same value. When you start increasing r beyond 3 you start seeing oscillations. For example if you take r = 3.2 regardless of what x₀ you start with, you will eventually start alternating between about 0.513 and 0.799.  These oscillatory systems are still considered stable, but not in the same way as the simple system before. As you continue to increase r, you eventually start oscillating between 4 values, and then 8, and somewhere around r = 3.57, all hell breaks loose. Before we look at those crazy values, we should first look at what happens when r is greater than 4.  Here, regardless of what value of x₀ you start with, you will eventually shoot off into infinity.

So what happens between r = 3.57 and r = 4? After some large number of iterations you will wind up somewhere between 0 and 1, you will not shoot off into infinity. Exactly where though is impossible to predict.  The reason it's hard to predict is that even small errors in your initial value can bring you into wildly different places. For example, let's look at r = 3.6 and two different values for , one of which is 0.3 and the other is 0.301, a difference of one part in one thousand.What I've plotted below is the difference between our two values as a function of iteration number.  Things seem nice and stable at the very beginning, but around generation 20, you start seeing very large differences between the two values. There's another period between about 35 and 45 where they are correlated, but after about 45 they diverge again. As time increases more this becomes even more chaotic and there is no correlation between the two values for any later generations.

Difference in the logistic map function for r = 3.7 when starting with 0.3 and 0.301

Now we get to what it actually means for the system to be "chaotic" as I described in the previous paragraph. For a system to be chaotic the error needs to be exponential.  The typical mathematical quantity used here is the Lyapunov Exponent, and this governs how chaotic a system behaves.  You can indeed calculate the Lyapunov Exponent for our system by fitting the curve before it starts exhibiting chaotic behavior. And you get a value of roughly 0.2.

It turns out many of the systems in the world exhibit chaotic behavior. One of the most familiar ones is the weather. Weather forecasting involves taking a lot of information from sensors around the globe and feeding them into complicated meteorological models in order to predict future weather.  However each of these measurements has some error, and even if all our measurements were perfectly accurate, we don't sample every molecule forcing us to fill in the gaps. Ignoring errors in our model, these sampling errors would eventually grow and dominate any system.  This is why forecasting the weather beyond a few days is usually useless. It also explains the butterfly example shown above. It's not that the butterfly literally causes a tornado, but rather a small error, such as that caused by not considering the motion of a butterfly's wings, can eventually cause the entire global weather system to deviate from prediction after enough time. 

Some chaotic systems only display the behavior after very long times. It turns out that the planetary motions of Venus and Mercury are chaotic due to the gravitational forces exerted by all the other planets. We can predict the motion of Venus and Mercury only to about 4-5 million years. The planetary system is governed by extremely simple laws, and there are only a finite number of objects to consider. Yet, it turns out that all you need is 3 planetary bodies to create a chaotic system.

One question I have always wondered about is whether the human brain is chaotic.  It's not something I've ever gotten a good answer too, but perhaps with some extra research, it can be a topic for the future.

Quantum Uncertainty

If you are ever trading incredibly nerdy jokes, here's one you can offer up.

Werner Heisenberg is driving in his car when a cop pulls him over. The cop asks, "Do you know how fast you were going?" To which Heisenberg replies, no clue, but I know exactly where I am.

If this joke made sense to you, great. If it didn't, hopefully it will after you read the rest of this section. Heisenberg is notable for many physical concepts, but the one referenced here is commonly referred to the Heisenberg Uncertainty Principle. It basically states that there is a minimum error to which you can know something. The error in a particle's momentum multiplied by the error in the particle's position must be greater than some number.  How big? About 5.27 * 10^-35 m²*kg/s. Just in case you're not familiar with the notation, that's 0.0000000000000000000000000000000000527.  Really small.

However it turns out that this fundamental error can actually matter in reality. Let's see how.  I give you a single atom of radon-222. That's a nucleus with 86 protons and 136 neutrons. If you've ever had radon detection in your basement, it's looking for this guy.  At some point in the near future, this radon nucleus will eject an "alpha particle" which is a small nucleus of two protons and two neutrons (a helium-4 nucleus) leaving a polonium-218 nucleus. When will it eject it? That I can't tell you. But what I can tell you is the probability that it will have ejected the alpha particle at some point in time from now. Specifically I can tell you that there's a 50% chance that in 3.82 days, it will have ejected the alpha particle.

Let's say one day has passed and the radon molecule has not decayed, how long will it be until it has a 50% chance of decaying? If you said 2.82 days, you are wrong. It's still 3.82 days. The past is irrelevant, all that matters is the current state.

So what's actually going on? Generally when people picture nuclei they thing of a solid ball of protons and neutrons glued together. This is how they're often displayed in science textbooks. But that's misleading. The protons and neutrons are not fixed in location, they're moving. They are held together by the strong nuclear force and pushed apart by electromagnetic repulsion (among other things).  Peering into the nucleus itself is impossible, that's because the scales are small enough that Heisenberg's Principle comes into play. One way to picture the decay is to imagine that glob of 2 protons and 2 neutrons existing somewhere in the nucleus and bouncing around. Be aware, this is not exactly what's going on, just use it as a simplified model. Usually when our glob gets to the edge the strong nuclear force pulls it back in. At some point though, it gets just enough energy that it manages to escape out. Since we can't peer into the nucleus we have no idea when this might happen for any given nucleus beyond the probabilities that we learn from observing many different nuclei.

The alpha decay of a radioactive nucleus is an example of a fundamental uncertainty that we can't do anything about. We are limited by fundamental laws of physics and are forced to deal with our radon nucleus entirely probabilistically. In most real world applications you are not dealing with a single nucleus but rather a very large number of nuclei. In these cases statistics are your friend and you can very accurately predict that in 3.82 days half of your large number of radon molecules will have decayed. Yet, a single alpha particle is detectable, and it is possible to engineer situations where that decay of the single radon molecule matters.

When we combine quantum uncertainty with our knowledge of chaotic system we run into a situation where many systems cannot be predicted at all beyond a certain time. There is a limit to how accurate we can measure something, and even small inaccuracies can cause big differences given enough time. It is very important to keep these effects in mind when people lament about how eliminating active gods who are manipulating parameters behind the scenes creates deterministic worlds. It appears our universe has indeterminism built into the very fabric of it.

Going back to the joke we started with. If you don't get blank stares, you can continue with the following response to Heisenberg's wisecrack:

The cop, clearly having none of it, punches Heisenberg. "Ow," says Heisenberg "do you know how hard you hit me?" "No," says the cop, "but I know exactly when I did it."

Why this is funny is left as an exercise for the reader.

Can Anything be Fully Understood?

In the last two sections we talked about uncertainties in physical measurements. The results came along with real world analogies and it was fairly obvious we are talking about how stuff happens in the universe we inhabit. It turns out, that even in artificially constructed systems, there are things that evade understanding. This is a somewhat profound thought. Even when you strip away all the messy issues that come about with real world data, stuff like measurement errors, chaotic systems and quantum uncertainty, and limit yourself to purely mathematical systems. There are still things that you just can't know.

This idea comes from perhaps one of the most misunderstood mathematical theorems, due to the fact that it's more often discussed by philosophers than mathematicians. I'll gladly add myself to the list of non-mathematicians who probably misunderstand Goedel's Incompleteness Theorem.

According to my understanding the theorem states the following. Let's you have a set of consistent axioms, like for example those involving real numbers, addition and multiplication. Then you can use this set of axioms to evaluate whether a statement is true or not. For example, you could verify that 2+3=5 using the definitions of integers and addition. Goedel's Incompleteness Theorem states that there are statements that are true in this system that cannot be proven from the axioms alone. 

Like all modern mathematics, Goedel's theorem is precise in what it actually says. And I have been somewhat less precise, since precision often prevents understanding to non-mathematicians (including me!)  But I think this gives a general gist of what's going on. The important point in the purest of mathematical systems, uncertainty abounds. It is something we can't get away from, so we best learn to live with it.

Summing up

Hopefully I've convinced you that uncertainty is something that we're stuck with. Running after 100% certainty is a fool's errand, there are lesser certainties that are good enough. How close is good enough depends greatly on the system. In a chaotic system it turns out that even 99.9999999% isn't good enough given long enough times. In a stable system, or over shorter time scales, you can get away with far less certainty.

I might also have convinced you that there are weird and amazing things to discover in the universe. I hope to revisit some of these in the future. I hope you'll join me for those excursions as well. 

Finally, I predict (with 95% certainty) that in the not too distant future someone will comment that I've misstated Goedel's theorem.