# Fine-tuning Is a Red Herring Approximately 26 experimentally determined constants occupy key roles in the equations of fundamental physics. Scientists have determined the values of these constants by careful measurement, and they appear like glistening apples in the tree of theories that make up mathematical physics. Using the formulas bearing these constants, one can compute values and compare them to measurements made directly on the physical world. For example, the fine-structure constant (approximately 1/137) allows one to correctly calculate the properties of fundamental particles and their interactions, leading to chemistry and biology and therefor most of observed reality on earth. The fine-structure constant shares a crucial property with its companions, namely that even a slight difference in its value would produce a universe much different from the universe we observe. Were the constant slightly larger or smaller, chemical bonds could not form (as far we know), leaving the universe as a soup of isolated particles. Most of the other constants have a similar role – even minor variations in their values would result in a universe without us or much else. But here we are, chemical bonds and all, and here are those pesky constants. Where did they come from? Constants arise in the interplay between theoretical and experimental physics. Conceptually, a researcher will propose a mathematical structure that seems to reflect the behavior of some set of observations. However, that mathematical structure, usually one or more equations, has some leeway built in in the form of constant values sprinkled through the equations. By comparing the experimental results to the pattern described by the equations, one can adjust the constants until the results agree with the calculations. This is the sense in which the physicist "tunes" the equation. Albert Einstein's General Theory of Relativity is a wonderful historical example of this process. Through deep physical intuition (and help from a few mathematicians) Einstein was able for formulate the equations governing gravity in a very general form.[^1] The equations included a constant, $\lambda$, called the "cosmological constant". At the time Einstein was working it was thought that the universe was static, neither expanding or contracting. Einstein added the constant to tune the equations to imply a static universe. Later he regretted the move, calling it his "greatest mistake". Except that astronomers discovered in the 1990s [^2] that the universe was anything but static, rather it is expanding at an ever-increasing rate. Adding back the constant with a certain value matched the expansion beautifully. Indeed, if $\lambda$ were a tiny bit smaller than the currently accepted value there would be no galaxies, or the Big Bang would have been a tiny *pop*. The philosophical discussions around these constants go by the moniker "fine-tuning" arguments. The phrase "fine-tuning" suggests "tuning" which suggests something that tunes. Perhaps the universe is tuned to allow our existence by a god, a variant on the well-known Argument from Design. However, philosophers such as Philip Goff[^3] make a weaker claim: fine-tuning suggests that the universe has a purpose, or *telos*. Said purpose may or may not be provided by a god, so Goff's claim is weaker than common design arguments. It only asserts that in some cosmic sense the universe has purposefully "chosen" the values of the constants to make us and our environment possible. Rather than explore the pros and cons of the fine-tuning arguments, I want to question the usefulness of engaging in such arguments at all. The observation of (so-called) fine-tuning – namely the presence of these measured constants in *current* theories of fundamental physics – adds nothing to the more fundamental question "Why is there anything at all?". Let us take a slight detour to discuss the constants of nature, that is, the constants that appear in mathematical formulations of physical laws. There are two fundamentally different types - experimental constants and mathematical constants. Experimental constants are discover by, you guessed it, experiment. They are *contingent* on the facts of nature discovered empirically. I have mentioned a couple of them already, the fine-structure constant, $\alpha$, and the cosmological constant, $\lambda$. Other examples include the mass and the charge of an electron and many much more obscure. Mathematical constants are those that arise in pure mathematics independent of any experiments. A prototypical example is the famous number $\pi$, the ratio of the circumference of a circle to is diameter. More mundane examples include 1 and 0. One of the most beautiful mathematical formulas of all time is Euler's formula linking $\pi$, 0 , 1 and two other numbers: *e* (the base of the natural logarithms) and *i*, the square root of -1. $ e^{i\pi} + 1 = 0 $ Another notable example is the golden ratio, which happens to show up in many biological forms but has several roles in mathematics. Such mathematical numbers are known *a priori* ( "in advance") rather than discovered experimentally. Suppose we refer to the collection of mathematically expressed theories of physics as $\mathcal{T}$ . In its current formulation, $\mathcal{T}$ has embedded in it some 26 constants known only by experiment, together with the mathematical constants found in Euler's formula (and possibly others). As our scientific knowledge progresses, we may discover that there are relationships among the formulas that establish relationships between the fine-tuning constants so that one may be expressed in terms of the others. Thus as we learn more 26 might become 25, or 24, …., as our mathematic representation matures. Suppose as $\mathcal{T}$ evolve, we whittle down the number of fine-tuning constants to just one, call it "$\Omegaquot;. Imagine – one constant with an experimentally measured value that must be *exactly* what has been measured or the universe goes haywire! This may currently seem implausible but it is certainly possible. The fine-tuning argument would still be in play – the universe intended $\Omega$ to hold its current value just so the universe can exist as it currently does. Fair enough: any fine-tuning argument that works today would work for the one-constant case, too. Now go one step further and suppose that we elide $\Omega$, that last bothersome measured constant, so that the new and improved $\mathcal{T}$ contains only mathematical constants such as $\pi$, *e*, *i*, etc. That means that the laws of physics are *a priori* pure mathematical structures. Some physicists think of this as the Holy Grail, showing that the universe behaves strictly according to non-contingent laws. As audacious as this result may sound, does it defeat the fine-tuning argument suggesting calling for a *telos*? I think not. Even if the laws that govern the behavior of the physical universe are *a priori* – strictly mathematical – they are still laws that govern the *relationships* among the elements of material reality. The universe is populated with *stuff*, and the question remains, "what the stuff"? Isn't this question the true underlying force of the fine-tuning argument, namely that there is some purpose for the universe being the way it is, except now we don't have any annoying constants to worry about, just existence itself. Yet the same question remains: is there some purpose behind Being itself? Why is there anything? As Steven Hawking asks,[^4] what breathes fire into the equations? Worrying about fine tuning doesn't add anything to the question. [^1]: Carroll, Sean. The Biggest Ideas in the Universe: Space, Time, and Motion. New York: Dutton, 2022. [^2]: Nobel Prize Committee. “The 2011 Nobel Prize in Physics.” NobelPrize.org, October 5, 2011. <https://www.nobelprize.org/prizes/physics/2011/press-release/>. [^3]: Goff, Philip. Why?: The Purpose of the Universe. Oxford: Oxford University Press, 2023. [^4]: Hawking, Stephen W. A Brief History of Time: From the Big Bang to Black Holes. London: Bantam Press, 1988, p. 174.