Zero—Much to Do About Nothing?
Zero and Nothing. They sound like such simple words, but have you ever thought about what they actually mean? When a calculation results in zero, one takes a second look. Why can’t you divide by zero? When zero appears as a multiplier in a long equation, all other terms, no matter how complex, magically vanish leaving zero as the result. When you read a food label that says zero sugar, zero pesticides, or no additives present, what does that really mean? When a rocket countdown reaches zero, liftoff occurs! You would not want to be at ground zero in an epidemic or explosion. How do you feel when the balance of your bank account is zero in contrast to the feeling of securing a zero-interest no-fee credit card? When asked what your friend is doing, nothing may be their answer but then one often becomes suspicious. What does emptiness connote in philosophy, and does the concept of nothingness have significance to you?
I have always been fascinated by the concept of and definition of zero. The idea of nothing, as well as its assignment to the specific number 0, is encountered in many fields ranging from philosophy to mathematics, as well as the pure sciences of physics and chemistry to its practical application in areas including toxicology, food safety, statistics, finance, and the law. We are constantly exposed to zero in areas far beyond mathematics where we are tempted with zero calorie soda to credit cards with zero percent interest. In gambling, the placement of 0 and 00 on the roulette wheel ensures that the house has the advantage since the most common bets of red or black and even or odd lose when the ball lands on a zero. Other counting numbers do not share this unique aura. One could make an argument for the noninteger numbers π and ∞, but zero easily assumes greater prominence and consternation in wide ranging swaths of human endeavor.
Philosophy
Zero is a misfit amongst the normal so-called counting numbers. It defies definition as it reflects nothing, emptiness, or a void. The ancient Greeks abhorred the concept of emptiness and the void. Zero causes headaches when first encountered in arithmetic, where one is forbidden to divide by it. Zero occupies a unique position in our numbering system as it is the only counting integer that does not relate to any actual quantity. It came into existence centuries after all the counting numbers were introduced in civilizations across the world, originating in first millennium India and only then migrating to Europe in the 13th century. It first appeared as a placeholder in the numbering schemes of many civilizations and only later assumed its place as a true number.
Zero was inextricably linked to the void and nothingness, beliefs that often engendered fear and even chaos.
Nothingness and emptiness were and remain central constructs of major schools of both Eastern and Western philosophies and religions. Psychologically they can be the drivers of anxiety and depression in the West or the enlightened goals of meditative peace in the East. The concept of nothingness arose simultaneously in the fifth century BCE in ancient China, India, and Greece, embodied in the philosophies ranging from Taoism to nihilism. Zero was inextricably linked to the void and nothingness, beliefs that often engendered fear and even chaos. The Greeks had no zero in their mathematics nor did they believe the void was possible. Its concept bleeds into the interpretation of the fourth century BCE Greek philosopher Zeno’s famous paradox. It only started to abate when post-Socratic philosophers, including the atomists Leucippus and Democritus had to accept emptiness as the space between atoms, a concept carried forward in history by Lucretius who strongly influenced later natural philosophers. Even Aristotle did not believe that 0 and 1 were true numbers, with his first number being 2. The concept of nothingness and nihilism continue in the modern and contemporary eras embedded in philosophies including: Buddhism, Hinduism, skepticism, existentialism, and poststructuralism. Hindu philosophers are crucial in understanding the concept of nothingness and probably the first emergence of zero. In Hinduism, emptiness or nothingness relates to the vastness that is the source of creation, a concept that mirrors modern quantum physics. The concept of nothing continues to have a strong hold on the human mind.
These discordant perspectives still affect the interpretation of using the digit 0 today. When interpreting 0 as nothing or empty, all sorts of contexts derived from numerous encounters with it subconsciously haunt our cognitive processes affecting our perspective on the issue at hand and influence how we arrive at a conclusion. This powerful meme suggesting cautiousness still hangs on.
Mathematics
Zero is a crucial number in mathematics. The simplest definition is that it is the origin point of the number line, dividing positive and negative numbers.
However, one should note that in the timeline of history, there is no year zero separating the current (CE) from ancient (BCE) eras!
The most serious issue with zero is its limitations and distinctive properties in certain mathematical operations. These unique properties are what drives modern anxiety when a calculation results in a zero. As mentioned, zero occupies a unique place in our number system as an integer not representing any value. Due to some interesting properties, if zero finds itself in the denominator of a function or as the exponent of a number (Y), strange things happen. We know we cannot take the logarithm of zero. Division by zero (Y÷0 or Y/0) is not possible, it is undefined. Multiplying by zero erases the value of the number being multiplied (Y × 0 = 0). Zero factorial equals one (0! = 1). Raising anything to the power of zero results in the expression having a value of one (Y^0= 1), except if it is zero being raised to the zero power (0^0), which is also not possible. Calculus developed a partial fix for this with the concept of limits, where the value of a function is estimated as it approaches zero.
With the very recent release of generative AI programs, scraping zero values from the web … could provide misleading and even dangerous conclusions.
I was also motivated to undertake this journey due to my involvement in artificial intelligence (AI) and machine learning projects, where data are “scraped” from the open web and then used for calculations, removed from the context of the original study that generated the data. I have seen large data studies where 0 simply appears in a dataset because there was no value entered. It is the default entry. Calculations from these data generate the feared message: ERROR. Many calculations and modeling studies performed in science use a logarithmic transformation of the data being studied. If you try to take the logarithm of zero, the computer freezes. The author has seen error messages such as “The logarithm of zero is undefined because it is not a real number.” Experienced workers are aware of this and curate the data into a database before analysis. Naive analysts are not so fortunate. With the very recent release of generative AI programs, scraping zero values from the web and using them as meaning zero could provide misleading and even dangerous conclusions unless the data are first curated. One should provide an operational definition of zero to ensure such misuse doesn’t occur. Yet this operational definition rarely gets permanently associated with the data for which it was defined. There are no meta tags attached to data elements providing a definition that would stay attached, because that zero entry has now moved and entered a calculation for which it was never intended.
Toxicology, Finance, and Chemical Food Safety
It’s easy to count distinct things such as people, apples, and money. What about chemicals and the risk of adverse health effects after exposure to them? Does the absence of a chemical in food, termed a residue, mean there is no detectable chemical using the most sensitive methods of modern chemistry, or does it mean just not enough chemical to cause you ill health effects? The issue is understanding how zero is to be measured, interpreted, and employed relative to the problem on which one is working. Are we discussing the absence of any pharmacologic or toxicologic effect, or the limit of quantitation or detection in analytical chemistry? This sorting process requires great discipline and effort to parse out the different baggage (vocabulary, definition, methods, sensitivity, rules, purpose) associated with zero or nothing as applied to the different disciplines involved in the analysis, to get the contexts involved straight, and to achieve a rational and deliberative solution.
Zero is a misfit amongst the normal so-called counting numbers. It defies definition as it reflects nothing, emptiness, or a void.
Even in fields such as finance, where the concept of measuring zero in the context of financial worth is consequential, it becomes more complicated once one moves from assessing wealth by counting coins or paper currency to estimating market values of real estate, antiques, or complex securities and other financial instruments that depend on the state of the market and economy when they are eventually cashed in and counted. Zero in this case is the placeholder, much as in the number line, that divides one’s net worth as having assets versus being in debt or even on the verge of bankruptcy. Such monetary transactions and asset counting in trade were the original driving force behind the development of numbers by ancient civilizations.
Although one can endlessly debate the impact and significance of a number relating to nothing, problems arise when one must measure zero and attest that nothing is there. A simple example is illustrative. Zero sugar soda is easily defined as sugar not being added in its manufacture. However, if a natural beverage is to be labeled as such, there must be proof that analysis would yield a result of zero. But how precise does that need to be, what type of sugar is being assayed, and how much variability is there in natural beverages? This analytical zero is the source of confusion in its use today.
This concept of low but safe chemical and drug residue concentrations has been studied and well defined by modern toxicology. However, very low concentrations of chemical residues may still be detected in food well below the levels of concern by the extremely sensitive tools that modern analytical chemistry has to offer. When I first started working in this field over 40 years ago, the allowable safe concentration, termed a tolerance, was very close to the analytical limit of detection. Now, advances in chemistry detect compounds orders of magnitude below any possible biological effects, and far below regulatory tolerances established when the drugs or pesticides used were first approved. We are constantly exposed to very low levels of numerous natural compounds in our daily lives that may have no significant effect at the levels presented because our biological defense systems, honed by evolution, allow us to easily eliminate or metabolize these compounds to a harmless product. Problems often arise when consumer groups conduct market surveys of food products and look for and report on detectable, not violative, chemical residues. This is where analytical chemistry, toxicology, regulatory, and trade policies clash.
Although one can endlessly debate the impact and significance of a number relating to nothing, problems arise when one must measure zero and attest that nothing is there.
How do scientists derive the toxicological endpoints that find their way into regulatory doctrines? This involves defining what no biological effect means, that is nothing happens, after exposure to this concentration of chemical in food. The analytical limit of quantification and limit of detection define detectability while tolerance and maximum residue level define absence of biological effect. These are two distinct domains. The limits for biological effect are a prediction of human safety based on experimental studies generally conducted in lifetime animal toxicology trials that determine the no adverse effect level (NOAEL) or benchmark dose (BMD). In the scheme depicting this below, it must be stressed that the starting point is the level where no effect was seen in experimental long-term exposures. This concentration is then further reduced by large safety factors (10× to 100×) to protect against uncertainty in making these extrapolations. When a chemical is detected below these final regulatory endpoints, there is no safety concern.
The endpoint is different when drug assays are used to regulate sports doping. Here detection proves exposure and thus potentially illegal drug use. There is no safety endpoint. In detection of alcohol in people, there is alcohol detection in a minor (which is illegal) versus quantification in an adult (which only prohibits levels related to intoxication), because adults are allowed to consume alcohol at levels determined not to affect driving ability. In sports, drug testing is a detection issue.
In toxicology risk assessment, especially in detecting potential carcinogens, threshold concentrations are based on estimations using various risk assessment models that extrapolate to lower concentrations from the available experimental data obtained at higher concentrations. The laboratory animal studies are lifetime exposures at a tolerable dose. In many cases, tumors are only seen at the highest dose studied, yet a low dose with significant safety factors is still generated.
Depending on the nature of the chemical being regulated and the legal jurisdiction involved, numerous safe and action levels are employed. Different tolerances and maximum residue limits vary across different regulatory jurisdictions for the same drug or pharmaceutical product. All assume lifetime consumption at this concentration, not a one-time exposure in a violative salad ingredient at lunch! It must be mentioned that allergens present a different issue than true chemical toxins, as their mechanism of action is different. These are handled by regulatory agencies as indicating their presence in a product and suggested avoidance by sensitive individuals.
Tension arises when a chemical, such as a pesticide, is found in food at levels well below the acceptable tolerance but still at a measurable amount. There is no quantifiable biological risk to exposure at this concentration despite their detection in food. Regulatory agencies acknowledge this in their definition of a threshold, which already incorporates multiple safety factors and assumes lifetime consumption. There are hundreds of other natural compounds and toxins that may be present at higher levels in food that are not even looked for since they are natural organic constituents, yet do not produce an adverse effect. The average diet contains over a gram and a half of natural pesticides and phytotoxins. Yet when chemicals in a food basket survey are detectable, and often not even quantifiable, the media often report this as “dangerous chemicals were detected in the food.” Many of these are agricultural chemicals, including pesticides, that are important to large-scale agriculture and are used to improve crop production, ward off plant diseases, or kill true toxin-producing fungi (e.g., mycotoxins). A hazard may be present to the manufacturer or pesticide applicator, but the minuscule level present in food is safe.
Zero is a unique number both in mathematics and in how its interpretation affects everyday life.
The apple is my favorite example of a food loaded with both nutrients and toxins. Apples are one of many fruits whose seeds contain acute toxic doses of cyanide compounds. Apples, olives, and coffee also contain caffeic acid, the potential rodent carcinogen. Pitted fruits, such as apricots and peaches, and even sweet almonds contain the cyanogenic glycoside amygdalin. When was the last time you picked up an apple or apricot that contained a warning label indicating a potential for toxin exposure? An interesting sidebar is that although caffeic acid may be a potential carcinogen, exposure to it from its various sources has never detected any evidence for carcinogenic effects in humans.
The issue fueling the public concern about chemical exposure in food and the environment is one of miscommunication. There is no universally accepted definition of zero. Both the context in which it was determined and the problem to which it will be applied must be taken into consideration. The proper approach is to operationally define what is meant by zero and the conditions under which it is assigned.
Grocery surveys often only report detection independent of what the allowable limits may be. Internet searches then determine that the chemical detected may be harmful, but no one looks at the dose where any adverse effect was seen versus the level of contamination detected. This is termed “regulation by hazard.” The public must be made aware of this as the situation will only worsen with increasingly sensitive analytical methods. The chemicals haven’t changed. Focus should be on issues with a higher positive public health impact. Unfortunately, in today’s political climate, these issues are not openly and freely debated.
So, to Make Something Out of Nothing …
Zero is a unique number both in mathematics and in how its interpretation affects everyday life. In some scenarios, zero simply means nothing or empty. No apples, no money. In other cases, it is an analytical determination based on measurement, and interpretation of its meaning is dependent upon extrapolations from experimental models. In other cases, it is the result of a risk assessment where consuming a chemical at a concentration less than its tolerance produced zero adverse health effects. All these steps are steeped in uncertainty but are biased toward overestimating adverse risks.
There are similarly fascinating concepts of zero and nothing in physics and astronomy where one tries to define absolute zero temperature, zero space, or the smallest time interval. These are beyond the scope of this brief introduction.
I started this journey into zero because I have wrestled with its meaning my entire professional career. It is a number that is mathematically unique and even peculiar at times. It psychologically harbors connotations and emotions that are simply not associated with other numbers. I wanted to try and better understand how this psychological angst arose and further probe the meaning of zero and nothing in biology and especially food safety. My concept of zero did not seem to match that reported by the media and on social platforms. Why has the meaning of zero become so complicated? I now appreciate where some of this confusion arose and how nothing indeed became quite something.
And finally, as the Dalai Lama has written: “A zero itself is nothing, but without a zero you cannot count anything; therefore, a zero is something, yet zero.”
This essay was adapted by the author from Zero—Much to Do About Nothing published by Springer in 2025.