This is my pizza recipe

I make pretty good pizza. I came up with this through trial and error, and now I want to share it with you. But first, lemme share a picture of one of my pizzas just to get you in the mood.

How I make the dough

I used Tipo 00 pizza flour. The brand I like is called Anna Napoletana, but I'm sure other stuff works. It's finer than all purpose flour, and it has a higher protein/glucose content. If you can't find it, you can use bread flour. That's the next best thing. It's a little more coarse, but it has about the same protein content. As a last resort, you can use all purpose flour. I like King Arthur's. Here are the proportions I use (these are called baker's percentages):

Flour - 100%
water - 65%
salt - 2%
active dry yeast - 1%

I use these proportions because it makes it easy to remember, easy to calculate in my head, and it works. I have gone as high as 70% on the water content. It makes a good dough, but it's more difficult to work with. I usually make enough dough for two pizzas at a time. Or, if I'm making pizzas for some other people, I'll make enough for four. I'm just going to tell you what the measurements are for one pizza. You can just multiply this yourself if you want to make more.

Flour - 210 grams
water - 137 grams
salt - 4 or 5 grams
active dry yeast - 2 grams

It's a really good idea to get a digital scale so you can get these proportions exact. It also allows you to experiment by varying them a little and keeping track of what you did.

EDIT (8/8/2023): What the hey, I'll just do the math for you. . .

Two pizzas
Flour - 420 grams
water - 273 grams
salt - 8 or 9 grams
active dry yeast - 4 grams and maybe a smidge more

Three pizzas
Flour - 630 grams
water - 410 grams
salt - 13 grams
active dry yeast - 6 or 7 grams

Four pizzas
Flour - 840 grams
water - 546 grams
salt - 17 grams
active dry yeast - 8 or 9 grams

I mix that up in a bowl, then turn it out on the counter. I use a bowl scraper to get everything out. Then I mix it the rest of the way with my hands. As soon as it starts getting just a little sticky, I cover it with the bowl and walk away for 10 minutes. Then I come back and knead it until I get tired of kneading it. That's usually about five to ten minutes. Ideally, it will stop being sticky after a while. Do not add flour to it. If you want, you can let it rest another ten minutes and come back to kneading it. It should be less sticky that way. But kneading it ought to make it less sticky eventually.

Once it's fairly smooth and not so sticky anymore, put it in the bowl, cover it with plastic wrap, and stick it in the oven with the oven light on. Leave it in there until it doubles in size. It may take an hour or two, depending on how cold it is in your place. If your yeast isn't good anymore, it may not rise much at all. I keep my yeast in the refrigerator so it stays good longer.

Once it has doubled in size, take it out, and fold it over a few times, and turn it into a ball by tucking it under itself, stretching it. Then stick it back in the bowl, cover it, and stick it back in the oven until it doubles again.

This time, make your dough balls. First, put a little olive oil in a decent sized bowl. You can use tupperware if you want, but I prefer a bowl. Cut up the dough if you made enough for more than one pizza. Tuck it under itself over and over, stretching the top. There are YouTube videos showing how to do this part. It's easier show than to explain. Put the dough smooth size down in the olive oil, spin it around a little so the olive oil gets all over that side, then flip it over and spin it a little more. Put some plastic wrap over that, but not too tight because you want it to have room to rise a little.

Leave that out a few minutes - no more than 5 or 10 - then stick it in the refrigerator. Leave it in there for two days. You can use it after one day or even three or four days, but it's best after two days.

How I make the sauce

I get one of those big cans of San Marzano whole peeled tomatoes. You can fish the tomatoes out with your hand if you want to, but I just pour the whole thing into a mixing bowl and use it all. You can use a hand blender if you want. I prefer not to because it's too easy to over do it. If you over do it, it'll be too runny. I prefer to squeeze the tomatoes with my hand and just mush them up. I want it to be slightly chunky, and doing it with my hand gets just the right consistency.

We want to add some ingredients to it for flavour. I don't usually measure my ingredients, but I guess I'll give you some measurements to get you in the ballpark. There's lots of flexibility in these proportions, though.

Olive oil - No more than a quarter of a cup. Probably a little less.
Sea salt - I'm not really sure how much. Maybe 10 grams.
Oregano - I use that dry stuff you buy in a shaker and just about cover the top of my sauce. It's a lot.
Garlic - I use two or three cloves. I don't know what you call it, but I rub them against this little grater thingy.
Red pepper - I'm not really sure how much red pepper I put in there. Just take a guess, then taste it and see if you like it.

I told you I was going to give you some measurements, but I didn't really do that, did I? Sorry. It's subjective, but it's unlikely you'll create a disaster.

Anywho, put that in some tupperware and put it in the refrigerator.

I've complained about the fact that this makes so much sauce it commits me to having to eat nothing but pizza for two weeks. It's enough sauce for about ten pizzas. It has been suggested to me that I freeze it in little zip lock snack bags so I can take them out one at a time to use it. I've tried that, and it always ruins the sauce. It makes it runny, and it's just never as good. You can try it, though.

How I put my pizza together

On the day I make the pizza, I take the dough out of the refrigerator about two hours before it's time to make it. I sprinkle a little flour on top of it, and some flour on the counter or cutting board. I scoop it out with my bowl scraper, and gently put it smooth side down on the flour I sprinkled on the counter. I don't put any flour on the rough side which should be facing up. I cover it with a big bowl and let it sit for two hours, or thereabouts.

At least an hour before I'm ready to make the pizza, I turn my oven on to the highest temperature it will go. Where I used to live, that was 500ºF. I've made pizza at other people's houses, though, and theirs only got up to 450ºF, which was a bummer. Anyway, the point here is to heat up your pizza stone. You need to have a pizza stone.

Now that the oven is hot, and the dough has come to room temperature and risen a little, it's time to put the pizza together.

You're going to need a pizza peel. I put a dusting of flour on the pizza peel so the pizza doesn't stick. A lot of people like to use semonila, and that's probably better. You can use corn meal if you want, but I'm not crazy about that. The idea is just to make sure the pizza doesn't stick to the peel.

Now we need to stretch the dough. Again, this is easier to show than to explain, so watch some YouTube videos. Basically, I use my finger tips to push down the middle of the dough and out toward the edge. I leave the edges fluffy. Do not use a rolling pin like some idiots do because you'll destroy your crust. Once the middle is pushed down, and the puffy perimeter is pretty even, I pick it up and begin to stretch it. I lay it over one hand, pull a little with the other, then rotate it, and pull again. As it grows, I'll put my knuckles under it and stretch it out a little more. If I'm feeling it, I'll toss it in the air and spin it.

Once you're done playing with the dough, put it on the pizza peel. Now stetch it by pushing it, pulling it, or whatever you have to do to get it nice and round. If you dusted your peel like you should have, this step should be easy.

Now take a big plastic spoon, scoop some pizza sauce, and pour it in the middle. Use the back of the spoon to spread it. Start in the middle, and make circles, getting bigger and bigger each time you go all the way around until you've spread the sauce pretty evenly over the pizza. A lot of people use too much sauce when they're just learning to make pizza. Again, I can't really explain how much to use. It's easier to show.

Considering how much I say that, maybe I just need to make a YouTube video.

Anyway, pick up the pizza peel and shake it back and forth a little bit to make sure the pizza slides without sticking. If it doesn't, lift it close to where it's not sliding and throw some flour under there, and try again. Once you get it sliding well, slide it onto that pizza stone. You can really mess up here. Don't freak out if you mess up the first time. After you do it a few times, it gets easy. You can make it perfectly round.

Keep that oven light on and watch it. When the edges just barely start to change colour, take it out using the pizza peel.

At this point, you can put whatever you want on it. I almost always put some parmesan on it first. Sometimes, I just put fresh mozzarella on it and nothing more. If you get shredded mozzarella from the grocery store, it's not going to be that great. Fresh mozerella is awesome possum. Other times, I'll cut up some ham and put it on there, and I might put some pineapple on it. That's how I roll. I've also been known to put mushrooms on it. Anchovies and pineapple go well together. The contrast of the saltiness with the sweetness is good. I might even put some sauteed onions on it. You just never know. One thing I don't do is pile on a whole bunch of different toppings. I use two at the most. If I make it for other people, I'll put sausage or pepperoni on it, but I'm not crazy about that. Get some fresh mozzerella if you can find it. It is possible to make it, though, and there are YouTube videos about it. Just tear it up with your hand and put it on the pizza.

Stick that back on the pizza stone, and cook it until all the cheese is melted and the crust is a nice golden brown. I can't give you a time because I don't know how the laws of physics operate in your particular oven. But just watch it. You know what a pizza is supposed to look like when it's done.

Once it's done, take it out, put it on a rack, let it cool a couple of minutes. At this point, I'll sometimes put some fresh basil on it. It goes great with a plain cheese pizza. Finally, transfer it to a cutting board, cut it up, and eat it.

You're welcome.

Are philosophical zombies coherent?

One argument against thought experiments involving philosophical zombies is that philosophical zombies are incoherent, and I half way agree with that.

Consider two people, both named Bob. To distinguish them we'll call them Bob Normal (Bob_N) and Bob Zombie (Bob_Z). Physically, Bob_N and Bob_Z are identical. Atom per atom, they are exactly alike. They look the same, behave the same, say the same things, etc. To keep them from occupying the same space at the same time, let's put them in separate worlds that are also identical.

Identical, that is, with one exception. Bob_N is conscious and Bob_Z is not.

Some folks think this is an incoherent scenario, and I agree. It's incoherent whether you assume physicalism or dualism. Let me explain why each scenario is incoherent.

Let's assume physicalism

If physicalism is true, and Bob_N is conscious, that would mean the physical structure of Bob_N's brain is what's giving rise to his conscious experiences. If Bob_Z has the exact same physical structure as Bob_N, then it would be impossible for Bob_Z not to be conscious. That makes the scenario incoherent.

Let's assume dualism is true

If dualism is true, then the explanation for why Bob_N is conscious and Bob_Z isn't is because Bob_N has a soul and Bob_Z doesn't. Much of Bob_N's behavior is the result of causal interactions between his brain and his soul. Since Bob_Z doesn't have a soul, the same interactions are not going on in his head, and it is impossible that they behave the same way. That makes the scenario incoherent.

So either way you look at it, a scenario in which Bob_N and Bob_Z are physically identical and behave in exactly the same way is an incoherent scenario.

So how can the idea of a philosophical zombie contribute anything to the subject of dualism vs. physicalism? Some arguments rely on the possibility or conceivability of philosophical zombies to make their point, but I don't think that's necessary. A hypothetical scenario doesn't have to be possible to serve as an illustration. For example, Aristotle imagined what a world would be like without the law of non-contradiction. There would be no significant or meaningful speech or action in such a world. His point doesn't depend on such a world being possible.

In the same way, I think philosophical zombies can be invoked to illustrate how physicalism leads to epiphenominalism which, in turn, undermines physicalism, even if philosophical zombies are impossible. Here's a basic outline of the argument.

If physicalism is true, then all of our behavior (including our vocalizations) can be accounted for solely by reference to the third person properties of the brain and its parts, plus the laws of nature. You can explain exhaustively why somebody behaves in a particular way without ever referring to anything like a motive, belief, idea, desire, thought, plan, perception, etc. With that being the case, our behavior would be exactly the same even if these first person experiences didn't exist. Nevermind whether it's possible for them not to exist given our actual brain states. The point is that if our behavior would be the same in their absense, that means they don't contribute to our behavior. But that is absurd, so physicalism is false.

One objection somebody might raise to the above argument is that explaining behavior in terms of physics vs. psychology are just two ways of explaining the same thing. They are two layers of abstraction. It's similar to the difference between explaining the output of the computer in terms of functions like addition and subtractions as opposed to explaining it in terms of current, voltage, and the properties of electrons and various computer components.

But the same thing applies here. It is not because two and two actually make four that your calculator spits out that result. It would spit out that result even if the circuits didn't happen to represents the number two or the process of addition. You can program a computer to spit things out that are meaningful to us, but their meaning is irrelevant to the process by which the computer spits it out. It takes a conscious engineer and programmer to make a computer that spits out what, to us, is meaningful information.

In the same way, even if conscious experience is somehow the same thing as physical brain stuff obeying the laws of physics, it wouldn't matter one bit what those conscious expereiences are about. If some brain state associated with a sensation of burning resulted in jerking your hand away from a hot skillet, it would result in that same behavior even if it happened that the brain state was associated with a different conscious experience or no conscious experience at all. Under phyiscalism, it isn't by virtue of what our conscious experiences are about that results in our behavior. Rather, it's just the underlying physical substrate that produces our behavior whether the associated conscious experiences were about something different or absent altogether.

And that's just cray cray. I think the philosophical zombie thought experiment is useful to illustrate this even if they are not actually possible for the reasons I gave above.

Besides all that, it seems to me that artificial intelligence shows how something like a philosophical zombie could exist. Something resembling a human could exist that behaves just like a human, including having conversations and showing physiological behavior we usually associate with expressions of emotion without actually being conscious. If such a machine ever became conscious, we'd probably have no way to know it.

The a priori two step

There are a handful of things we know by intuition that are not necessary truths. Most other things we know depend on us knowing these handful of things. They include, but are not limited to, morality, the external world, the past, other minds, and the uniformity of nature. But within these intuitions, there are actually two things to know about each of them.

Morality

1. We know that there is a real objective difference between right and wrong.
2. We know some particular behaviors are right and others are wrong.

The external world

1. We know that there is an external world.
2. We know that particular things we perceive are part of the external world.

The past

1. We know the past actually happened.
2. We know some particular memories we have correspond to what happened in the past.

Other minds

1. We know there are other minds.
2. We know there's a mind behind the behavior of particular people and sometimes animals.

The uniformity of nature

1. We know the future will resemble the past.
2. We know that particular things will happen in the future because we've observed them repeatedly in the past.

In each of these categories, we are less sure about the particulars of the second items of knowledge than we are the first. In fact, we make mistakes when it comes to the second items of knowledge all the time. However, in each case, the fact that we can often be wrong with regard to the second is never a sufficient reason to doubt the first.

The fact that people disagree on morality, and the fact that we sometiems change our moral point of view shows that we often have incorrect beliefs about right and wrong, but that is no reason to doubt that there is such a thing as right and wrong.

Most of the time when we dream, we think everything we are perceiving is real, but none of it is. When we are awake, we see illusions and mirages. Some people experience hallucinations, phantom limb syndrom, or they hear things. Even in the case of people with psychosis who experience more than the usual amount of faulty perceptions, that is never a reason to doubt the existence of the external world entirely.

I've lost count of how many times I've heard people say, "Memory is notoriously unreliable." While I think that view is overblown, it is true that our memories often fail us. It's not just that we are forgetful. It's that we remember things differently than they actually happened. If you've ever been in a relationship for a significant period of time, you've probably had an argument over how something happened because you each remember it differently. I'm sometimes surprised when I read what I wrote in my journal years ago to discover things happened a little differently than I remember. Our memories are very fallible. However, that is no reason to embrace Last Thursdaism or doubt that there even was a past.

People are notorious for anthropomorphizing--attributing human traits (e.g thought and emotion) onto inanimate things. We also attribute the wrong mental states to things that have minds. We misread each other and misunderstand each other, but it's even worse when we project human traits onto other animals. Some people err in the opposite extreme and think animals have no thought or emotion. Some even go so far as to think animals are not conscious at all. With some bugs and worms, it's hard to even know if they have any conscious experience. However, the fact that we make all of these mistakes when trying to understand the minds (or lack of minds) of others is no reason in the world to doubt that there are other minds.

Hasty generalization is a fallacy we've all been guilty of at one time or another. It's probably the main reason superstition exists. We make generalizations by extrapolating from too few instances. We've all done it. Also, we often under-generalize. We refuse to learn from past experience. We can be stubborn and think next time will be different. However, the fact that we often make mistakes when reasoning inductively is no reason at all for us to doubt the validity of inductive reasoning.

Our confidence in the first item of knowledge under each category is why we exert so much effort toward being right about the second.

We debate moral issues and engage in moral reasoning because we think there are correct and incorrect answers to moral questions.

We rub our eyes when we suspect we're seeing things or ask others, "Did you hear that?" when we think we might've heard a suspicious noise. We do this to weed the bad perceptions from the good perceptions because we think there's a real world out there, and we want to make sure we're seeing it as it really is.

We write things down, look for corroberating testimony or evidence, strain our brains to remember how things really happened, and we retrace our steps in an effort to clarify our memories. We argue with people who remember things differently because we know that something happened. It's just a matter of finding out what.

When we initially notice patterns, we test them to see if they continue to repeat, and if so, under what circumstances. We formulate laws that describe in a mathematical way how we should expect the world to operate from here on out. We test these laws by making observations, and we extrapolate from the test to the rest of the world. If water boils at the same temperature under the same pressure every time we run the test, then we assume that's just the way water is, and it should apply just as well to samples of water we haven't tried to boil. We do these experiements because we know that experience can tell us what we should expect the world to be like going forward.

Most of the things you know, or think you know, can be traced back to these handful of a priori truths or truths like them. Others I didn't go into include causation, the law of parsimony, the notion that ought implies can, the reality of time, an enduring self, intentional action, object permanence, and the reliability of our cognitive faculties in general. For most people, the knowledge of these things is so automatic that they never even think about them. The knowledge runs in the background. But if you thoughfully ask, "Why do you think that?" for almost any random thing you know about the world, and you keep asking, you will eventually trace the belief back to one or more of these items of a priori knowledge.

Usually, that's where the line of inquiry stops. These items of knowledge are part of the foundation of all knowledge. They aren't inferred from something prior. The information is just built into us. We're hard wired to believe these things. Since these items of knowledge come pre-loaded into the brain of every reasonably developed human mind, and they are not inferred from evidence or argument, we know them by intuition. Intuition is immediate knowledge upon reflection. We don't turn our gaze outward to see if these things are true; rather, we turn our gaze inward and simply see what is written on the mind.

There are some people who attempt to find something even more foundational than these items of knowledge. They'll try to come up with reasons for why we should believe them other than intuition. However, the reasons always turn out to be less obvious than the truths themselves. That casts doubt on whether those reasons are what actually justify the beliefs or lead to the beliefs. Even if any of these attempts at arguing for one of these truths is a sound argument, the argument is probably not why we actually believe those truths.

It is possible for each of these things to be false. After all, none of them are necessary truths. But just because something is possible doesn't mean it's reasonable to believe. In the case of these a priori truths, it is unreasonable to doubt them, especially the first item of knowledge under each category. But that doesn't stop some people.

The normalizability objection to fine tuning, take one

Timothy and Lydia McGrew and Eric Vestrup published a paper called "Probabilities and the Fine-Tuning Argument." They came up with an objection to the argument from fine-tuning that's based on the fact that you can't specify the probability of a finite range of values over an infinte range of possibilities. The reason is because the probability wouldn't be normalizable.

According to the principle of indifference, if you don't know what the probability distribution is over some range of values, then you assume an equal probability distribution. That is, you assign an equal probability to each possibility. For example, if you had a six sided dice, and you didn't know if it had been ground in such a way as to make it more likely to land on 2 than on 3, then you assume it has an equal chance of landing on any side. Each side would have a 1 in 6 chance of landing face up. Since each side has a 1 in 6 chance of landing face up, and there are six sides in all, then if you add the probabilities for each possible outcome, the total is 1.

1/6 * 6 = 1

If the probability distribution is not even, then whatever the probability of each side is, they should still add up to 1. The reason is because all the possibilities added together sum up to a guarantee. If you roll the dice, some side is guaranteed to face up. Otherwise, you haven't accounted for all the possibilities.

That's what it means for a probability distribution to be normalized. It means the individual probabilities of all the possibilities add up to 1 or 100%.

It is possible to normalize a probability distribution over an infinite range of possibilities, though. Consider a convergent series that sums to 1, such as this:

1/2 + 1/4 + 1/8 + 1/16 + . . . + 1/infinity = 1

So if you had a probability distrubtion over an infinite range of possibilities in which the possibilities were put in one to one correspondence with that convergent series, you could normalize that probability distribution.

If you were using the principle of indifference, though, then you couldn't noramlize the probability distribution over an infinite range of possibilities. First of all, the probability of each member would be 1/infinity, which is zero. Second of all, even if it weren't zero, but was some small finite number, the probabilities of each possibility wouldn't sum to 1. It would sum to infinity.

Another related problem is that if the range of possible values is infinite, then the probability of any finite range within the total range would be infintesimal. That would render fine-tuning meaningless because no matter how big the life permitting range of some value is, as long as it's finite, the universe would still be fine-tuned. 1/n approaches zero as n approaches infinity, but the same thing is true of 10⁵⁰⁰/n. It doesn't matter how big the life permitting range is. If the range of possible value is zero to infinity, the probability of getting something in any finite-sized life permitting range is still infintesimal. To paraphrase Syndrome, "If everything is fine-tuned, then nothing is."

Luke Barnes, an astrophysicist from Australia, published a philosophical paper responding to the normalizability objection. The paper is called "Fine-Tuning in the Context of Bayesian Theory Testing." Most of this paper is over my head, but after furrowing my eyebrows and twisting my hair around my finger, I think I have gotten a handle on one particular paragraph on the bottom of page 7 of his paper that I want to talk about today.

I'm going to use the rest mass of an electron to explain, as best I can, how we can limit the possible range of values in order to normalize the probability distribution of those values. Basically, we can limit the range by what makes sense within the theories that describe the electron.

Bear with me. There's going to be a little math. Nothing too difficult. Also, just as a disclaimer, Luke doesn't go into all this math in that paragraph. Once I thought I understood what he was saying, I went and crunched the numbers to see for myself. Physics makes more sense to me if I can see the math. This is my attempt to break it down and explain it to you in a way that's more detailed and easier to understand (I think). If there are mistakes in these details, they are mine, not Luke's.

There are two theories that come into play in this explanation. There's quantum mechanics, and there's general relativity. According to general relativity, if you condense a given amount of mass to within a certain radius, it will become a black hole. The radius at which a given mass becomes a black hole is called the Schwarzschild radius. Here is the equation for the Schwarzschild radius:

R = 2mG/c²

m = mass
G = the gravitational constant = 6.6743 x 10^-3 N*m²/kg²
c = the speed of light = 299,792,458 m/s

The rest mass of an electron is 9.109×10^-31 kg, which is 0.511 MeV. We can plug that into the equation to calculate the Schwartzschild radius for an electron.

R = (2 * 9.109x10^-31 kg * 6.6743x10^-3N*m²/kg²)/(299,792,458 m/s)² = 1.35x10^-49 meters

That's pretty small. Nobody really knows how small an electron actually is, though. There were some experiments where they bounced some electrons off of each other. They tried to figure out how big they were by looking at the scattering pattern, but it looked like they were point particles with no size at all. You'd think that if an electron were that small, it would be a black hole. If it has no size, but some finite mass, then it's density would be infinite. Zero radius is well within the Scharzschild radius. So what the what, you ask?

Well, that's where quantum theory comes into play. In quantum theory, the size of an electron is defined by it's Compton wavelength.

λ = h/mc

h = Planck's constant = 6.626x10^-34 joule-seconds
m = mass
c = the speed of light = 299,792,458 m/s

Instead of running the calculation this time, let's just get the Compton wavelength off the internet. For an electron that's 2.426×10⁻¹² m. Notice the Compton wavelength of an electron is many orders of magnitude bigger than its Schwartzschild radius. That's why the electron is not a black hole.

But suppose the electron was more massive. Well, there's a limit to how massive an electron could be before it becomes a black hole. To figure out what that limit is, let's set the Schwartzschild radius equal to 1/2 the Compton wavelength and solve for mass.

2mG/c² = (1/2) * (h/mc)

So, m = Sqrt (hc/4G)

m = Sqrt ([6.626x10^-34 J*s x 299,792,458 m/s]/[4 * 6.6743 x 10^-3 Nm²/kg²]) = 2.73x10^-12 kg

In case you're worried about the units, 1 Joule is 1 kg*m²/s² and 1 Newton is 1 kg*m/s². The units works out. Don't worry. I did this on paper first. It's that total that might be wrong in case I made a typo in my calculator.

Notice that all of this just takes quantum theory and general relativity to their logical conclusions and predicts the highest mass an electron could have before becoming its own black hole. In reality, it's hard to say what would happen if an electron were that massive. Quantum mechanics and general relativity conflict on those kinds of scales, and we need a theory of quantum gravity to know what really happens.

But what this shows, according to Luke Barnes, is that there is a finite range of values an electron can take before our theories start to break down. Beyond that range, we can't trust quantum mechanics and general relativity. If we want our theories to make sense, then we have to place a limit on the range of possible values various constants can take. In the case of the electron, we can limit the possible range from zero to 2.73x10^-12 kg. Zero is a natural place to put the lower limit because negative mass doesn't make much sense. But if you don't like that, then you could put the lower limit at -2.73x10^-12 kg. Either way, we'd have a finite range of possible values, and that would allow us to normalize our probability distribution.

According to Luke Barnes, what I just showed with the electron can also be done with other constants. For constants that have units, like the mass of an electron, Luke says we can use the Planck scale to define a finite range of possible values to the constants. The Planck mass is actually bigger than the mass I calculated, so either Luke is being generous, or I've made some mistake. For constants that don't have units, we can limit those ranges in other ways that I didn't go into in this blog post. He went into that in his paper, too.

There's a lot more to Luke's paper, and most of it I don't understand. What I just explained was my interpreation of the last paragraph on page 7 of his paper. If you read his paper, and you get to that paragraph, please leave a comment and tell me if you think I've misunderstood something or if I made some mistake.