Why We Shouldn't Exist: A Table of 18 Anthropic Requirements

Cross-posted from www.futureandcosmos.blogspot.com

The Standard Model is regarded as a highly “unnatural” theory. Aside from having a large number of different particles and forces, many of which seem surplus to requirement, it is also very precariously balanced. If you change any of the 20+ numbers that have to be put into the theory even a little, you rapidly find yourself living in a universe without atoms. This spooky fine-tuning worries many physicists, leaving the universe looking as though it has been set up in just the right way for life to exist.
Harry Cliff, Particle Physicist, in a Scientific American article

If you have not read much on the topic of the anthropic principle and the issue of possible fine-tuning in the universe, it may be hard to follow the topic. Discussions typically involves subatomic physics, cosmology, biology, evolution and some other subjects that don't exactly make light reading. I think that the topic will be easier to understand if we condense it into one simple table that summarizes the most relevant facts. I have created such a table, which appears below.

The left column of the table lists various items that appear in nature. The right column lists requirements of those items. The table is in chronological order. It starts out with requirements that must be met in the very beginning, near the time of the Big Bang, if the universe is ever going to end up with people like us, inhabitants of a technical civilization living near a sunlike star. Towards the end of the table are items that appeared billions of years later in time. The final item in the table is “Civilizations near sunlike stars.” It is interesting that for the last item to come into existence, all of the previous items in the list must previously come into existence. I have added color coding which makes the various interlinked dependencies much easier to follow. 

 

Click to Expand

I will now explain why each item has the requirements I have listed.

Row 1 (Higgs field): The Higgs field (related to the Higgs boson) is said to give mass to other particles. Scientists are puzzled by why the Higgs field has the strength it has, and they say that it seems to require fine-tuning to 15 decimal places. This is a problem called the hierarchy problem or the naturalness problem. It is discussed in this scientific paper entitled The Higgs: so simple yet so unnatural. As a Daily Galaxy article put it, “Using theory as it currently stands, the mass of the Higgs boson can only be explained as the result of a random fine-tuning of the physical constants of the universe at a level of accuracy of one in one quadrillion.”

Row 2 (up quarks and down quarks, electrons): The particles in the nuclei of atoms (protons and neutrons) are made up of smaller particles called up quarks and down quarks. A requirement of the large-scale existence of up quarks and down quarks (and also electrons) is what scientists call matter/antimatter asymmetry (a situation where matter is vastly more abundant than antimatter). This is a puzzle to scientists, because the standard model of physics seems to predict that matter and antimatter should have existed in equal amounts at the time of the Big Bang, which would have caused both types of particles to collide with each other and convert into energy, leaving almost nothing but energy in the universe. A requirement for electrons is the Higgs field, and on this page a physicist says that the electron would not have mass without the Higgs field. 

Row 3 (protons, neutrons): The simple requirement is that there be up quarks and down quarks, discussed in the previous paragraph.

Row 4 (hydrogen atoms): The requirement for a hydrogen atom is that you have one proton and one electron, and also the electromagnetic force, the force of attraction between a proton and an electron. Without that force, electrons would not have any tendency to orbit a nucleus.

Row 5 (galaxies): Galaxies are huge collections of stars. There are many requirements for the formation of galaxies after the Big Bang. The universe had to begin with a fine-tuned expansion rate, as a slighter higher rate would have caused an expansion too fast for galaxies to form, and a slightly slower rate would have caused all matter to collapse into superdense black holes. Scientists also say that numerous other things had to be just right (the other items listed in this row). One requirement is primordial density perturbations greater than .000001 and less than .0001, as explained here. One particularly severe requirement seems to involve dark energy, which is regarded pretty much the same as the cosmological constant. Cosmologists conclude that the level of dark energy seems to have been fine-tuned to something like 1 part in 10⁶⁰ or one part in 10¹²⁰. The issue, called the vacuum catastrophe, has been fretted over by many physicists. This paper refers to the “tremendous, unsolved naturalness problem” posed by the cosmological constant.
 
Row 6 (carbon atoms): This row refers to the abundant existence of carbon atoms, something which ends up having lots of requirements. Besides the previously mentioned requirements for the hydrogen atom (protons, electrons, and the electromagnetic force), there are the additional requirements of the neutron and the strong nuclear force (the two of them allow you to have a carbon nucleus that holds together, despite the mutual repulsion between the protons). There is also the requirement that you have a law of nature called the Pauli Exclusion Principle, something that is quite necessary for both solid matter and complex carbon bonds. Then there is an additional requirement for something called nuclear resonances, which assures that carbon is produced in abundant quantities by stars through a process called the triple alpha process. Without this additional requirement, there would not be enough carbon (which wasn't produced in the Big Bang). This point has been widely discussed by scientists such as Hoyle, and in this scientific paper stating that a 0.4% change in one parameter would have left us without a universe abundant in both carbon and oxygen. An additional requirement that I had no space to list in my table is the requirement that the neutron mass be higher than the proton mass.

Row 7 (oxygen atoms): Oxygen atoms have all the same requirements of carbon atoms, including the same special requirement involving nuclear resonances, necessary for oxygen to be produced by stars in abundant amounts. The scientific paper here argues that there would not be much oxygen without the weak nuclear force, so I have also listed that as a requirement. 

Row 8 (Heavier atoms): By heavier atoms I mean all atoms than have more than about 25 protons (which includes copper, lead, silver, gold, zinc, tin, and probably also iron). These types of atoms have most of the same requirements of carbon atoms and oxygen atoms, except that to have these atoms in abundance you don't need nuclear resonances but instead the stellar explosions called supernovae explosions (explosions of stars that produce heavy elements such as lead and iron). These supernovae explosions require a tiny particle called the neutrino and a force called the weak nuclear force.

Row 9 (Sunlike stars): I may define sunlike stars as those that are white, yellow, or orange (or some combination of those colors). Sunlike stars require galaxies (since if galaxies had not formed, there would be no stars). Sunlike stars also require a very delicate fine-tuning of some of the most fundamental constants of nature. The physicist Paul Davies says on page 73 of The Accidental Universe: “If gravity were very slightly weaker, or electromagnetism very slightly stronger (or the electron slightly less massive relative to the proton), all stars would be red dwarfs. A correspondingly tiny change the other way, and they would all be blue giants.” Blue giants are too-short lived for life to evolve near them, and red dwarf stars are not believed to be as favorable for life's evolution as sunlike stars. 

Row 10 (water): Water requires oxygen atoms and hydrogen atoms, as we can tell from its formula H₂0. Because of its remarkable features that make it unique among liquids, there are probably additional requirements for water, but I haven't listed them.

Row 11 (stable planets): One requirement for stable planets is gravitation, the force that holds planets and stars together. But there is another very interesting requirement: that the electric charge of the proton exactly match the electric charge of the electron, to many decimal places. Electromagnetism (the fundamental force involving electric charges) is roughly 10³⁶ times stronger than gravitation, the weakest of the fundamental forces by far. Consequently a very slight mismatch between the charge of the electron and the proton would cause electromagnetism (roughly a trillion trillion trillion times stronger than gravitation) to completely overwhelm the gravity holding the planet together. In his book The Symbiotic Universe, astronomer George Greenstein (a professor emeritus at Amherst College) says this about the equality of the proton and electron charges: "Relatively small things like stones, people, and the like would fly apart if the two charges differed by as little as one part in 100 billion. Large structures like the Earth and the Sun require for their existence a yet more perfect balance of one part in a billion billion." In fact, experiments do indicate that the charge of the proton and the electron match to eighteen decimal places. 

A curious coincidence

Row 12 (nucleotides): Nucleotides are molecules that are the building blocks of RNA and DNA, molecules essential for life. Nucleotides require three types of atoms mentioned above (carbon, oxygen, and hydrogen atoms), as well as phosphorus atoms. They also require physics to be arranged in a way that allows for atoms to combine to make molecules consisting of multiple atoms.

Row 13 (genetic code): The genetic code is a semantic framework used by DNA and RNA, one in which particular combination of nucleotides stand for particular amino acids. The genetic code could roughly be called the software used by DNA and RNA. The origin of this code is one of science's great mysteries. We do not know how this code (required for all biological evolution) appeared from mere chemicals. This is the “code from chemicals” problem described in this blog post.

Row 14 (RNA): RNA is one of the two main molecules used by all living things, and it is believed to have preceded the more well-known and more complicated molecule DNA. It requires nucleotides (from which RNA is built), as well as the genetic code and water (as a substrate).

Row 15 (DNA): DNA requires nucleotides (from which it is built), as well as the genetic code and water. I also list RNA as a requirement since it is believed that RNA was a necessary predecessor of DNA.

Row 16 (Proteins, cells): Proteins are made by DNA and RNA using the genetic code. Requirements include water and amino acids (which I didn't list in the table for space reasons).

Row 17 (Photosynthesis): Photosynthesis is the process by which plants convert sunlight to chemical energy. Recent studies suggest that photosynthesis uses exotic quantum effects.

Row 18 (Civilizations near sunlike stars): Now we come to the last and most important row, which mentions civilizations such as our civilization. There are many requirements for such a civilization. All of the items on the 17 previous rows on the table are indirect or direct requirements of civilizations near sunlike stars. The well-understood direct requirements of such civilizations are heavier atoms (needed so that the civilization can have the metals needed for technology), sunlike stars, stable planets, proteins, cells, and photosynthesis (the last one being necessary even if the beings in a civilization ate nothing but meat, because they would still rely on a food chain that would require photosynthesis).

There is also a poorly understood requirement that does not occur previously on the list – the requirement that somehow unconscious matter can produce Mind of the type that humans have. That is a huge additional requirement. It may require additional laws of nature, or perhaps exotic features of quantum mechanics, as Penrose and Hameoff have suggested. Penrose and Hameroff say here that their “orchestrated objective reduction” theory “suggests that there is a connection between the brainʼs biomolecular processes and the basic structure of the universe,” and yesterday's news reported a finding that supports such a theory. The matter is still undecided, but we do seem to have a huge additional requirement from nature in order to go from mere cellular life to conscious life.

The table I have created illustrates the great number of intertwining requirements needed for the universe to be consistent with the eventual appearance of civilizations such as ours. A huge amount of fine-tuning is required to meet these requirements, most notably in rows 1, 5, 9, and 11, each of which require “1 in a trillion” type coincidences with a very low likelihood of randomly occurring, We also have the very mysterious requirements of rows 13 and row 18, both of which almost seem to require “blood from stone” type of requirements (row 13 involving the origin of the genetic code from chemicals, and row 18 involving the origin of human-like consciousness from mere matter).

The severe improbability of accidentally meeting all these requirements by chance is the reason I have entitled this blog post “Why We Shouldn't Exist: A Table of 18 Anthropic Requirements.” We can say that we shouldn't exist, in the sense that our existence seems to require an almost miraculous conspiracy of conveniences, coincidences and fine-tuning within nature. As Stephen Hawking and Leonard Mlodinow said in their book The Grand Design (page 161), “The laws of nature form a system that is extremely fine-tuned, and very little in physical law can be altered without destroying the possibility of the development of life as we know it.”

Why “Nature Has Math” Leads to “Nature Has Software”

It has long been recognized by many scientists that in a fundamental way nature seems to have mathematics embedded within it. One widely discussed essay that commented on this was a paper entitled The Unreasonable Effectiveness of Mathematics in the Natural Sciences, written by the physicist Eugene Wigner in 1960. Wigner pointed out numerous cases where scientists took to using mathematical formulas to describe some little understood feature of nature, and such an approach ended up being successful beyond their wildest dreams. An example is Isaac Newton coming up with the formula for gravitation based on earthly experiences and a few astronomical observations, a formula which has been used ever since, and still holds up today as we study distant galaxies (notwithstanding the additional complications of general relativity). Another example is Maxwell coming up with some equations to describe electricity and magnetism, which also proved to be the right equations for radio waves, which were not even discovered until decades later.

Wigner stated, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”

This paper provoked widespread comment, and since then it has widely been stated that nature has math within it in some fundamental way. Let's use this as the starting point for a line of reasoning.

Premise 1: It is widely recognized by scientists that in some fundamental way, nature has mathematics kind of embedded within it, as shown by countless cases in which mathematical formulas are the correct way to describe fundamental regularities in nature.

There are numerous fundamental formulas of physics that could be cited to support this statement, such as Newton's law, Coulomb's law, the Schrodinger equation, Einstein's equation for time dilation, and Einstein's famous equation e= mc². The nature of our universe is critically dependent upon such formulas.

Three formulas that dominate our universe

For an example of how impressed modern physicists are by the math within nature, you can look at this piece by physicist Max Tegmark entitled "Is the Universe Made of Math?"

Now let us consider: just what is mathematics? Mathematics is a very general term, which can refer to numbers, elements of geometry such as the circle and the circumference, and also simply logic, in the sense of mathematical algorithms and procedures. Most of what you learn in school when you study mathematics are procedures and algorithms for solving particular math problems.

In fact, mathematics seems to be mainly logic. Some famous philosophers such as Bertrand Russell and Alfred North Whitehead have argued that all mathematics can be reduced to logic, basically taking the position that math is just logic. A major branch of the philosophy of mathematics is called logicism, which maintains that all or most of math is just logic. So it therefore seems justified to state the next premise:

Premise 2: Very much of the math that we see operating within nature is a kind of logic.

If you doubt this premise, simply consider that almost every mathematical formula that appears in a physics text book can be stated in terms of logical statements such as “if/then” statements or algorithmic statements. For example, something such as Newton's law of gravity, which can be mathematically expressed by the formula shown above in the visual, can also be expressed by a logical statement such as “If two particles are separated by a particular distance, then the gravitational force of attraction between them is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, and also proportional to a universal constant G.”

Now let us consider: what type of logic is it nature is applying as it behaves the way we observe it to behave? The answer is that nature uses a very precise logic of complete regularity. By way of contrast, consider the way logic is used by an entity much less regular, for example, a bigoted Southern sheriff of the 1960's. Such a person might have used logic in all kinds of irregular and unpredictable ways, perhaps applying the rule “If I see someone littering, I'll arrest him” if the person aroused the sheriff's prejudices, or if the sheriff was in a bad mood, but completely ignoring the rule if the person was someone who looked like the sheriff, or the sheriff was in a good mood. But nature doesn't act in that kind of mercurial or unpredictable way. When it comes to things such as gravitation, electromagnetism, and the Pauli Exclusion principle, nature applies logic in a completely regular, invariant, precise, and predictable way. The Apollo moon landing in 1969 depended critically on gravitation acting in a completely regular, invariant, precise, and predictable way. The mission designers knew there was absolutely zero chance that the astronauts would ever suffer from a “bad gravity” day caused by gravitation working in an irregular way.

Another aspect of the logic used by nature is that it uses constants, certain fundamental numbers that are always the same. Below are some of the most fundamental constants used by nature.

Some fundamental constants of nature

So we must then state the next premise:

Premise 3: The logic we see operating within nature is a highly regular, invariant, precise, and predictable kind of logic, involving heavy use of fixed numerical constants.

Now we need merely ask ourselves: what are we talking about when we speak of the application of logic in a highly regular, invariant, precise, and predictable way, using numerical constants? This is not behavior that corresponds to the application of logic by human beings. Human beings are notoriously wavering and hard to predict, applying logic in all kinds of variant, biased, unpredictable, and inconsistent ways. The same political leader who will claim to be operating under fixed principles will then operate according to some other principles whenever it suits him politically.

But we do know of one type of system within our cities that does operate according to a highly regular, invariant, precise, and predictable kind of logic, making use of numerical constants. That system is a computer program. That leads to the next premise:

Premise 4: The application of logic in a highly regular, invariant, precise, and predictable kind of way, using fixed numerical constants, is a hallmark of programming.

This is the way computer programs operate. If I have a computer program that adds 1 to a total every time I press a key, the program will keep doing that with great regularity and predictability. It won't just do it 99 times out of 100. Computer programs also make use of fixed numerical constants, and all of the main programming languages have syntax support for declaring a constant within a program. For example, a computer program may have a line such as “const int AgeOfMajority = 18” which declares AgeOfMajority as a numerical constant. Then that constant will be used within the logic of the program, perhaps in a phrase beginning “if (AgeOfMajority >= 18).” 

It is a fair statement that nowadays when we see the application of logic in a highly regular, invariant, precise, and predictable kind of way, using fixed numerical constants, it is usually programming that we are seeing. 

Premise 5: It therefore seems that nature has programming.

This premise follows from premises 3 and 4, not as a matter of perfect certainty, but at least as a kind of likelihood (which is why I have used the word “seems”).

Now let's consider software. Is software something fundamentally different from programming? No. Most full-time software developers are called both computer programmers and also software developers. There's really no difference. So we can state this premise:

Premise 6: Software and programming are essentially the same thing.

Now from premise 5 and premise 6, this conclusion follows:

Conclusion: It therefore seems that nature has software.

This conclusion does not quite follow with metaphysical certainty, but this line of argument will do as a fairly simple bit of reasoning to support the claim that nature has built-in software.

For more elaborate arguments in support of the same conclusion that the universe must have built-in software, see my post The Theory of a Programmed Material Universe and my post Nature's Computation Needs Imply a Programmed Material Universe. 

As I explain in the first of these posts, once we realize that nature has built-in software, we can make much use of this idea as part of an explanatory framework, to help explain our universe's improbable evolution from an explosive beginning of supposedly infinite density to a place of fantastic harmony and order where life and Mind exist. 
 

Nature's Computation Needs Imply a Programmed Material Universe

Cross-posted from www.futureandcosmos.blogspot.com

Fasten your seat belt, because in this long blog post we will be blasting off to a bold new theory of the universe. Here is a visual preview:

Not wishing to build a castle floating in the air without any foundation, it will first be necessary to lay a solid foundation for this new theory. We can build that foundation by probing one of the most neglected and overlooked questions relating to nature. The question is: what, if any, are the computation requirements of nature? By this I mean: is it necessary that nature does some type of computation? If so, how much computation does nature need to do, and what elements of computation would nature need to satisfy such requirements?

The CRON Problem

Let's create an acronym to describe this problem. Let's call the problem the CRON problem. CRON stands for Computation Requirements of the Operations of Nature. We can define it like this:

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CRON Problem: Are there computation requirements in nature's operations -- things such as math that needs to be done, algorithms that need to be followed, or information that needs to be stored, retrieved or transferred? If so, roughly what is the level of computation that nature needs to do, and what elements of computation do we need to postulate to satisfy the computation requirements of nature?
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In the definition above (and throughout this post) I use computation very broadly to mean any phenomenon such as any operation involving calculation, the execution of rules or instructions, or the manipulation or transfer of information (as well as other additional actions that may be or seem to be goal-oriented, rule-based, or algorithmic, or which seem to methodically derive particular outputs from particular inputs, or which seem to involve the use or storage of data). According to this broad definition, your computer is doing computation when it is calculating some number, and it is also doing computation when you are doing a Google search or downloading a film.

The Biological Answer: There Definitely Are Computation Requirements, Which We Largely Understand

Let us first examine this CRON problem as it relates to biology. Imagine if you raised this CRON question to a biologist around 1930, asking him: are there computation requirements that nature must meet in order to perform the operations of biology?

I can easily imagine the answer the biologist might have given: “Don't be ridiculous. Computation is something done on pencil or paper, or by big bulky calculation machines. None of that goes on in the operations of biology.”

But we now know that this answer is false. Biology does require a large degree of computation, in the sense of information storage and information transfer. The main information storage medium is DNA. DNA uses a genetic code, which is a kind of tiny programming language. Every time a new organism is conceived and born, there's a transfer of information comparable to a huge data dump done by the IT division of a corporation. A gene is quite a bit like the complex variable known as a class in object-oriented languages, and each time a gene is used by an organism to create a protein, it is like the data processing operation known as instantiation.

This is a quite interesting example, because it shows a case of two things:

1. There was actually a huge computation requirement associated with a particular branch of nature (biology).
   
2. This computation requirement was overlooked and ignored by scientists in the field, who basically just failed to consider what the computation requirements were in the processes they were studying.
   

Now let us consider whether the same type of mistake is being made by modern physicists. Let us ask the fascinating question: are there computation requirements associated with nature's physics operations? By this I mean something like computation that must be performed by nature in order for the laws of physics to operate as we observe them operating.

Does Nature Need to Compute to Handle Relativistic Particle Collisions?

First let's look at a case that may seem quite simple at first: the case of two high-speed highly energetic protons colliding together, at a speed that is a good fraction of the speed of light (such a collision is called a relativistic collision). This is the kind of thing that happened very frequently in the early universe shortly after the Big Bang. It can also happen in a huge particle accelerator such as the Large Hadron Collider, where protons are collided together at very high speeds.

You might think that what happens in such a case is that the particles simply bounce off each other, as would happen if two fastball pitchers pitched fastballs at each other, and the balls collided. But if the two protons collide at a very high speed, a good fraction of the speed of light, something very different happens. The two protons are converted to other particles, perhaps many different particles. An example of this is shown below.

Now in regard to computation requirements, one might think at first that such a collision does not require any computation, since the end result is just a completely random mess. But actually nature follows an exact set of rules whenever such collisions occur.

1. The equation e = mc² is followed to compute the available mass-energy that can be used to create the output particles. (The actual “available energy” equation, involving a square root, is a little more complicated, but it is based on the e = mc² equation.)
   
2. Rules are followed in regard to the mass of the created particles. The created particles are always one of less than about 200 types (most short-lived), and each type of particle has some particular mass and some particular charge. It is as if nature has only a short list of allowed particles (each with a particular mass and charge), and nature only creates particles using that list, rather than just allowing particles of any old mass to be created (rather like a mother who only makes cookies by using a small set of cookie cutters). For example, we may see the creation of a particle with the mass of the electron, but never see a particle created with two or three or four times the mass of the electron. The stable particles that result from the collision (not counting antiparticles) are always either protons, neutrons, electrons, or neutrinos (or nuclei made from protons and neutrons). 
3. The collision follows a law called the law of the conservation of charge, which means that the total ratio of positive electric charge to negative electric charge is always precisely the same before and after the collision. This means, for example, that it is forbidden for you to have a collision of two protons (with a total of two positive electric charges) resulting in the creation of any set of particles that don't have a net total of two positive electric charges.
4. The collision follows a law called the law of the conservation of baryon number, which means that the total baryon number of the incoming particles is the same as the total baryon number of the particles that result from the collision.
5. The collision follows a law called the law of the conservation of lepton number, which puts further restrictions on the set of output particles that can appear as the result of the collision. This law is actually three laws in one, each relating to a particular type of lepton.

It seems that a nontrivial amount of computation is required for all of this to occur. If you doubt this, consider what would need to be done if you were a computer programmer trying to write a program that would simulate the results nature produces when two high-speed relativistic protons collide at a large fraction of the speed of light. You would need for your program to have some kind of list of the allowed particles that could appear as output particles, a list of less than about 200 possibilities, that would include the proton, the electron, the neutron, mesons, the muon, a few other particles, and their antiparticles (along with the masses and charges of each). Your program would have to compute the available energy for output particles, using an equation that would make use of a constant you had declared in your program representing the speed of light. Your program would also have to include some elaborate computation designed to calculate a set of output particles (derived using the list of particles) that satisfy the available energy limits and also the requirements of the law of the conservation of baryon number, the law of the conservation of charge, and the law of the conservation of lepton number. This would require quite a bit of programming to accomplish. It would probably take the average skilled programmer several days of programming to produce the required code to compute such a thing. It could easily take the programmer weeks to produce code that would perform these computations more or less instantaneously, without using a loop that uses a trial-and-error iteration.

So we seem to have come to a very interesting result here. It would seem that significant computation is indeed required by nature to handle events such as relativistic proton collisions. 
 

One can imagine a simpler universe in which high-speed protons always simply bounce off each other when they collide, like two baseballs which collide after being pitched by two fastball pitchers aiming at each other. That simple behavior might not require any computation by nature, but the very different type of behavior that happens in our universe when relativistic protons collide (involving a whole series of complicated rules that must be rigidly followed) does seem to require computation.

The creation of particles that occurs in a relativistic particle collision is actually strikingly similar to the instantiation of objects (using a class) that occurs in object-oriented software programming. Explaining this point would take several paragraphs, and I don't want this lengthy post to get too long; so I will leave this explanation for a separate future blog post on this topic.

Does Nature Need to Compute to Handle the Strong Force, the Weak Force, or Gravitation?

The preceding case may disturb someone who doesn't want to believe that nature needs to compute. But such a person may at least comfort himself by thinking: that's just a freak case; nowadays those relativistic particle collisions only occur in a few particle accelerators.

But now let us look at more general operations of nature, those involving the four fundamental forces of nature. Let us ask the question: does nature need to do computation in order to handle the fundamental forces that allow us and our planet to exist from day to day?

The four fundamental forces in nature are the strong nuclear force, the weak nuclear force, the electromagnetic force, and the gravitational force.

The strong nuclear force is the glue-like force that holds together the protons and neutrons in the nucleus of an atom. The range of this force is extremely small, so we don't seem to have a very obvious case here that a large amount of computation needs to be done for the force to work (although once we got into all the very complex calculations needed to compute the strong nuclear force, we might think differently).

The weak nuclear force is the fundamental force driving radioactivity. An interesting aspect of radioactivity is its random nature. It would seem that if you were to write a computer program simulating the behavior of radioactive particles, you would need to make use of a piece of software functionality called a random number generator. So it could be that nature does need to do some type of computation for the weak nuclear force to occur, but this is not at all the most compelling case where natural operations seem to require programming.

When we come to the gravitational force, we have a very different situation. It seems that for nature to handle gravitation as we understand it, insanely high amounts of computation are required.

This may seem surprising to someone familiar with the famous formula for gravitation, which is quite a simple formula. The formula is shown below:

 

In this formula, F is the gravitational force, G is the gravitational constant, m1 is the first mass, m2 is the second mass, and d is the distance between the masses.

Now looking at this formula, you may think: it looks like nature has to do a little calculation to compute gravity, but it's not much, so we can just ignore it.

But the fact is that the formula above is perhaps the greatest oversimplification in the history of science. The reason is that the formula is not the formula for computing the total gravitational forces acting on any single object in the universe. Instead, it is merely the formula for computing the gravitational force acting between one particle in the universe and any other particle in the universe.

To actually fully compute the gravitational forces acting on any one object or particle in the universe, we must do an almost infinitely more expensive calculation-- a calculation that must involve the mass of all other objects in the universe. This is because gravitation is an inverse square law with an infinite range. Every single massive object in the universe is exerting a gravitational force on you, and every other massive object.

I may note the very interesting fact that not one physicist in the history of science has ever done one billionth of the work needed to completely compute the complete gravitational forces attacking on any single particle or object.

To illustrate the computation requirement to calculate the gravitational forces acting on a single object, I can write a little function in the C# programming language:

void ComputeGravitationalForcesOnParticle (particle oParticleX)

{

   foreach (particle oParticleY in Universe)

   {

     double dForce = 0.0;

     double dTemp = 0.0;

     dTemp = (oParticleX.Mass * oParticleY.Mass) /

     ComputeDistanceBetweenParticles(oParticleX, oParticleY);

     dForce = GravitationalConstant * dTemp;

     ApplyForce(dForce, oParticleX);

   }

}

This is a function that takes one particular particle in the universe as an input, and computes the complete gravitational forces acting on that particle. It requires a loop, but the loop must run for a total of Z iterations, where Z is the total number of particles in the universe. So the loop must run for approximately 10⁸⁰ iterations (which is about the total number of particles in the observable universe). This means the loop must run about ten thousand billion trillion quadrillion quintillion sextillion times.

Now that's quite a bit of computation required. But for nature to do all the work needed to compute the gravitational forces on all particles in the universe during any given instant, it needs to do vastly more work than to just do the equivalent of running this function that is so expensive from a computational standpoint. Nature has to do the equivalent of a double loop, in which this loop is just the inner loop. To represent this in the C# language, we would need code something like this:

foreach (particle oParticleX in Universe)

{

  foreach (particle oParticleY in Universe)

   {

    double dForce = 0.0;

       double dTemp = 0.0;

    dTemp = (oParticleX.Mass * oParticleY.Mass) /

    ComputeDistanceBetweenParticles(oParticleX, oParticleY);

       dForce = GravitationalConstant * dTemp;

       ApplyForce(dForce, oParticleX);

   }

}

This is what is called a doubly nested loop, and programers know that doubly nested loops often become incredibly expensive from a computational standpoint. In this case the outer part of the loop must be traversed about 10⁸⁰ times, which is ten thousand billion trillion quadrillion quintillion sextillion iterations. But during each such iteration the inner loop must also be run 10⁸⁰ times. So the total number of times the inner part of the loop must be run is 10¹⁶⁰ which is ten thousand billion trillion quadrillion quintillion sextillion times greater than the total number of particles in the observable universe.

In any case in which you are calculating, say, once every second rather than a tiny fraction of a second, the calculation would have to be much more complicated, as it would have to take into account the relative motion between objects.

This makes it pretty clear that nature does indeed need to compute in order for gravitation to occur. It would seem that the computational requirements of gravitation are insanely high.

Does Nature Need to Compute to Handle the Electromagnetic Force?

The electromagnetic force is the force of attraction and repulsion between charged particles such as protons and neutrons. Like gravitation, the electromagnetic force is an inverse square law with infinite range. The basic formula for the electromagnetic force is Coulomb's law, which looks very similar to the basic formula for gravitation, except that it uses charges rather than masses, and a different constant. The formula is shown below:

In this formula F is the electromagnetic force of attraction or repulsion, k is a constant, q_a is the first charge, q_b is the second charge, and r is the distance between them.

The computational situation in regard to the electromagnetic force is very similar to the computational situation in regard to gravitation. Just as the formula for gravitation gives you only the tiniest fraction of the story (because it gives you a formula for calculating only the gravitational attraction between two different particles), Coulomb's law gives you only the tiniest fraction of the story (because it only gives you a formula for calculating the electromagnetic force between two particles). Since the range of electromagnetism is infinite, to fully compute the electromagnetic forces on any one particle or object requires that you take into account all other charged particles in the universe. If you were to write some C# programming code that gives the needed calculations to compute the electromagnetic forces acting on all particles in the universe, it would have to have an insanely expensive nested loop like the one previously described for gravitation. The code would be something like this:

for each (particle oParticleX in Universe)

{

   foreach (particle oParticleY in Universe)

    {

   double dForce = 0.0;

     double dTemp = 0.0;

   dTemp = (oParticleX.Charge * oParticleY.Charge) /

   ComputeDistanceBetweenParticles(oParticleX, oParticleY);

      dForce = CouplingConstant * dTemp;

     ApplyForce(dForce, oParticleX, eForceType);

   }

}

In this case the outer part of the loop must be traversed about 10⁸⁰ times, which is ten thousand billion trillion quadrillion quintillion sextillion iterations. But each such iteration requires running the inner part of the loop, which also must be run 10⁸⁰ times. So the total number of iterations that must be run is 10¹⁶⁰ which is a ten thousand billion trillion quadrillion quintillion sextillion times greater than the total number of particles in the universe.

It seems, then, that nature's computational demands required by the electromagnetic force are incredibly high.

I may note that there is a long-standing tradition of representing the charge of the electron as negative, and the charge of the proton as positive. But because the total number of attractions involving electrons is apparently equal to the total number of repulsions involving electrons, as far we can see (something that is also true for protons), there is no physical basis for this convention. When we get rid of this “cheat” that arose for the sake of mathematical convenience, we see that nature seems to have an algorithmic rule-based logic that it uses in electromagnetism, reminiscent of “if/then” logic in a computer program; and this logic differentiates between protons, neutrons and electrons. I will explain this point more fully in a future blog post.

Do Wave Functions Require Computation?

According to quantum mechanics, every particle has what is called a wave function. The wave function determines the likelihood of the particle existing at a particular location. You can get a crude, rough analogy of the wave function if you imagine a programming function that takes a few inputs, and then produces as an output a scatter plot showing a region of space, with little dots, each representing the chance of the particle being in a particular place. The more dots there are in a particular region of space, the higher the likelihood of the particle existing in that region. (The wave function is actually a lot more complicated that this, but such an analogy will serve as a rough sketch.)

But in order to do the full complete calculation of the wave function, this “scatter plot” must be basically the size of the universe. According to quantum mechanics, the wave function is actually “spread out” across the entire universe. This means that while the wave function is computing a very high likelihood that a particular electron now exists at a location close to where it was an instant ago, the wave function is also computing a very small, infinitesimal likelihood that the same electron may next be somewhere else in the universe, perhaps far, far away. Since the Pauli Exclusion Principle says two particles can't exist in the exact same spot with the same characteristics, this wave function calculation therefore must apparently take into consideration all the other particles in the universe.

Here is a quote from Cal Tech physicist Sean Carroll:

In quantum mechanics, the wave function for a particle will generically be spread out all over the universe, not confined to a small region. In practice, the overwhelming majority of the wave function might be localized to one particular place, but in principle there’s a very tiny bit of it at almost every point in space. (At some points it might be precisely zero, but those will be relatively rare.) Consequently, when I change the electric field anywhere in the universe, in principle the wave function of every electron changes just a little bit.

Again, we have a case where the computation requirements of nature seem to be insanely high. Every second nature seems to be computing the wave function of every particle in the universe, and the complete, full computation of that wave function requires an incredibly burdensome calculation that has to take all other particles in the universe into consideration.

I may also note that the very concept of the wave function – a function that takes inputs, and produces an output-- is extremely redolent of software and computation. Computer programs are built from functions that take inputs and produce outputs.

Does the Energy Density of a Vacuum Require Computation?

The case of empty space between the middle of stars may seem at first a case that requires absolutely zero computation by nature. After all, empty space between stars is just completely simple nothingness, right? Not quite. Quantum mechanics says that there is a vacuum energy density, and that the empty space between stars is a complex sea of virtual particles that last only for a fraction of a second, popping in and out of existence.

The mathematics required to compute this vacuum energy density is extremely complicated. Strangely enough, when physicists tried to calculate the vacuum energy density, they found at first that it seems to require an infinite amount of calculation to compute the energy density of the vacuum. So they resorted to a kind of trick or cheat called renormalization, which let them reduce the needed computation to a finite amount (Richard Feynman, the pioneer of renormalization, once admitted that it is “hocus pocus.”)

Even after this cheat, the required calculation is still ridiculously laborious, as it requires calculating contributions from many different particles, fields, and forces. The calculation required to compute the energy density of one cubic centimeter is very complicated and computationally expensive. Then that amount must be multiplied by more than a billion trillion quadrillion if we are to estimate nature's total computation requirements for calculating the vacuum energy density of all of the cubic centimeters in all of the empty spaces of our vast universe. So again we find a case where the computation requirements of nature seem to be very, very high.

Quantum Jumps and the Pauli Exclusion Principle: Do They Require Computation?

A quantum jump is one of the strangest things in quantum mechanics. A quantum jump occurs when an electron jumps from one orbit in an atom to another (or more strictly, from one quantum state to another). A quantum jump is typically triggered when an energetic photon strikes the electron. The following very crude diagram illustrates the idea. It shows an electron being struck by a photon of energy, with the electron jumping to a new orbital position. (I am speaking a bit schematically here.) 

A quantum jump

However, the actual jump does not occur as a journey from one orbit to another, as shown in this crude visual The jump occurs as an instantaneous transition from one orbit to another (or more precisely, from one quantum state to another). The opposite of the process depicted above also frequently happens. An electron will jump to an orbit closer to the nucleus, causing a photon to be emitted.

Now, in physics there is a very important law saying that in an atom no two electrons can have the same quantum state. This law is known as the Pauli Exclusion Principle. What this roughly means is that no two electrons with the same spin can have the same orbital state.

Imagine an atom with many electrons having many different orbits. In such a case a photon may strike an electron, causing it to jump to a new orbital position. But if the atom already has many electrons, the jump must occur in a way that obeys the Pauli Exclusion Principle. Depending on the intensity of the photon, the electron might have to jump over numerous different orbits, finding a slot for it to jump to that is compatible with the Pauli Exclusion Principle. 

A complex atom

For example, a photon might hit an electron in one of the inner orbits in an atom like the one depicted above, causing it to jump to one of the outer orbits (the distance would depend on how energetic the photon was).

But in this case the electron does not “try” various orbital positions, ending up in the first one that is compatible with the Pauli Exclusion Principle. Instead the electron instantaneously jumps to the first available orbital position (consistent with the photon energy) that satisfies the Pauli Exclusion Principle.

Now the question is: how does the electron know exactly the right position to instantaneously jump to in this kind of complicated situation? This is basically the same question that was asked by Rutherford, one of the great atomic physicists.

This seems to be a case where nature has to do computation, both to recall and apply the complicated law of the Pauli Exclusion Principle, and also to compute the correct position (consistent with the Pauli Exclusion Principle) for the electron to relocate. The whole operation seems rule-based and programmatic, and the quantum jumps resemble the “variable assignment” operations that occur within programming code (in which a variable instantaneously has its value changed).

Does Nature Need to Compute to Handle Quantum Entanglement?

Upon looking for further cases where nature seems to be performing like software, we might look at the famous double-slit experiment (in which electrons behave in a way that may suggest they are being influenced by some mysterious semi-cognizant rule). But let us instead look at an even more dramatic example: the phenomenon of quantum entanglement.

An example of quantum entanglement is shown in the illustration here. Particle C is a particle that decays into two daughter particles, A and B. Until someone measures the spin on either of these two particles, the spin of each of the daughter particles is indeterminate, which in quantum mechanics is a kind of fuzzy “not assigned yet” state (it might also be conceived as a combination of both possible spin states of Up and Down). It's rather like the same idea that one sees in a probability cloud diagram of an atom, showing an electron orbital, where rather than saying that the electron has an exact position we say that the electron's position is “spread out” throughout the probability cloud. Now, as soon as we measure the spin of either particle A or particle B, the spin becomes actualized or determined (one might may assigned, speaking as a programmer), and the other daughter particle then has its previously indeterminate spin become actualized, to a value that is the opposite of the spin value of the first particle. This effect has been found to not be limited by the speed of light, and seems to occur instantaneously.

Example of Quantum Entanglement

Does this effect seem to require computation? Indeed, it does. The phenomenon of quantum entanglement seems to require that nature has some database or data engine that links together each pair of entangled particles, so that nature can keep track of what particle or particles are associated with any particular entangled particle (rather in the same way that external databases keep track of which persons are your siblings or co-workers). Since physicists believe that quantum entanglement is not some rare phenomenon, but is instead occurring to a huge extent all over the universe, the total amount of computation that must be done seems to be immense.

This type of quantum entanglement effect bears no resemblance to anything we see in the macroscopic world, but something like this effect can be easily set up within a relational database. Using the SQL language I can easily set up a database in which particular objects can be inversely correlated. The database might be created with SQL statements something like this:

create table Particles

begin

ID1 int,

spin int,

mass decimal,

particle_type char(10)

end

go

create table Correlated_Particles

begin

ID1 int,

ID2 int

end

go

Now given such an arrangement of data, I could establish the inverse correlation by simply writing what is called an update trigger on the Particles table, which is a piece of code that is run whenever an item in that table is updated. This update trigger could have a few lines of code that checks whether a row in the Particles table has a match in the Correlated_Particles table. If such a match is found, another row in the Particles table is updated to achieve the inverse correlation. The code would look something like this:

CREATE TRIGGER Inverse_Correlation

ON Particles

AFTER UPDATE

AS

  declare @ID int

  IF ( UPDATE (spin) )

  BEGIN

   select @ID = ID2 from Correlated_Particles where

        ID1 = updated.ID1

   if (@ID is not null)

   update Particles set spin = updated.spin * -1 where ID1 = @ID

  END

GO

So we can achieve this strange effect of instantaneous inverse correlation, similar to quantum entanglement; but we need a database and we need some software, the code in the update trigger. To account for quantum entanglement in nature, we apparently need to postulate that nature has something like a data engine and some kind of software.

The Magical Infinite Free Computation Assumption (MIFCA)

Upon hearing these arguments, many will take a position along these lines: “Well, I guess nature does seem to be doing a great deal of computation, or something like computation. But we should not then conclude that the universe has any software, or any computing engine, or any data engine.” Such thinking kind of defies the observational principle that virtually all computation seems to require some kind of software, computation engine, and data engine (as suggested by the graphic below, which compares common elements of two very different types of computation, a paper and pencil math calculation and an online Amazon order). 

Elements Required for Complex Computation

I will give a name for the type of thinking described in the previous paragraph. I will call it the Magical Infinite Free Computation Assumption, or MIFCA. I call the assumption “magical” because all known computation involves some kind of software (or something like software) or some kind of computation engine or some type of data engine. To imagine that the universe is doing all this nearly infinite amount of computation every second without any software and without any computing engine and without any data engine is to magically imagine that nature is getting “for free” something that normally has a requirements cost (a cost in terms of the necessity of having a certain amount of software, a required computation engine, and a required data engine).

We can compare this type of MIFCA thinking to the thinking of a small child in regard to his parents' spending. A very young child may see his wealthy parents spending heavily all the time, and may generalize a rule that “My parents can buy whatever they want.” But such behavior actually has implications – it implies that perhaps one or both of the parents get a regular paycheck that gives them money, or that the parents have a bank account that stores their savings. But the small child never thinks about such implications – he just simply thinks, “My parents can buy whatever they want.” Similarly, the modern scientist may think that nature can do unlimited computation, but he fails to deduce the implications that follow: the fact that such computation implies the existence of an associated software and computation engine and data engine.

Although this type of MIFCA assumption may be extremely common, it does not make sense. To imagine that the universe does a nearly infinite amount of rule-based computation every second but without any software and without any computation engine and without any data engine is rather like imagining that somewhere there is a baseball game being continuously played but without any playing field and without any baseball and without any bases and without any baseball players.

The New Theory Forced Upon Us: A Programmed Material Universe

These examples (and many others I could give) suggest that nature does require a high degree of computation for the phenomena studied by physicists. We are led then, dramatically, to a new paradigm. In this paradigm we must assume that software is a fundamental aspect of the universe, and that in all probability the universe has some type of extremely elaborate programming, computing engine and data engine that is mostly unknown to us. (By using the term “engine” I simply some type of system, not necessarily a material one.)

I will call this theory the theory of a programmed material universe. I choose this name to distinguish such a theory from other theories which claim that the universe is just a Matrix-style illusion or that the universe is a simulation (perhaps one produced by alien programmers). I reject such theories, and argued against them in my blog post Why You Are Not Living in a Computer Simulation. The theory of a programmed material universe assumes that our universe is as real as we have always thought, but that a significant element of it is a computation layer that includes software. (I may note that the word “material” in the phrase “programmed material universe” is merely intended to mean “as real as anything else,” and does not necessarily imply any assumption about the nature of physical matter.)

We can think that software is a key element of the universe while still believing that physical matter is just as real as most people think. On our planet software controls imaginary virtual worlds such as the worlds of video games, but software also controls perfectly real physical objects such as robots and airplanes that are flying on autopilot. So if we assume that software is a key element of the universe, we can still continue to believe that the universe is every bit as real and material and physical as people thought it was in the 19^th century.

The fact that we do not understand the details of such a cosmic computation layer should not at all stop us from assuming that it exists. Scientists assume that dark matter exists, but purely because they think it is needed to explain other things, not because there is any unambiguous direct observational evidence for dark matter. If there are sound reasons for assuming the universe must have software and a computation engine and a data engine, then we should assume that it does, regardless of whether we know the details of such things.

An assumption that software is a key part of the universe also does not force us to believe in the weighty assumption that the universe is self-conscious. The software we are familiar with has a certain degree of intelligence or smarts, but it is not self-conscious. I can write a program in two hours that has some small degree of intelligence or smarts, but the program is no more self-conscious than a rock. So we can believe that the universe has a certain degree of intelligence or smarts in its software, without having to believe that the universe is self-conscious.

An assumption that software is a key part of the universe also does not force us to the simplistic conclusion that “the universe is a computer.” A more appropriate statement would be along these lines: the universe, like a Boeing 747, is a complicated system going towards a destination; and in both cases software and computation are key parts of the overall system. It would be inaccurate to say that a Boeing 747 is a computer, but it would be correct to say that software and a computing system are crucial parts of a Boeing 747 (used for navigation and whenever the plane flies on autopilot). Similarly we can say that software and computation are crucial parts of the universe (but we should not say “the universe is a computer.”)

One way to visualize this theory of a programmed material universe is to imagine the universe consisting of at least two layers – a mass energy layer and a computation layer, as schematically depicted below. We should suppose the computation layer is vastly more complicated than the simple flowchart shown in this visual. We should also suppose that the two layers are intertwined, rather than one layer floating above the other layer. If you ask "Which layer am I living in?" the answer is: both.

 One Way to Visualize the Theory 
 

The argument presented here (involving the computational requirements of nature) is only half of the case for the theory of a programmed material universe. The other half of the case (which I will explain in my next blog post) is the explanatory need for such a theory in giving a plausible narrative of the improbable events in the history of the universe. The universe has undergone an astounding evolution from a singularity of infinite density at the time of the Big Bang, achieving improbable and fortunate milestones such as the origin of galaxies, the formation of planets with heavy elements, the origin of life, and the origin of self-conscious Mind. Such an amazing progression is very hard to credibly explain outside of a theory of a programmed material universe, but such a progression is exactly what we would expect if such a theory is true (partially because software can be goal-oriented and goal seeking). Read my next blog post for a full explanation of this point.