This widely known thought-experiment is used to help us understand the principles of probability and randomness, and how chance can lead to unexpected outcomes. The idea has been referenced in pop culture from The Simpsons to Hitchhiker’s Guide to the Galaxy and on TikTok.

However, a new study reveals it would take an unbelievably huge amount of time — far longer than the lifespan of our universe, for a typing monkey to randomly produce Shakespeare. So, while the theorem is true, it is also somewhat misleading.

Mathematicians, Associate Professor Stephen Woodcock and Jay Falletta from the University of Technology Sydney (UTS), decided to examine the theorem using instead the limits of our finite universe.

“The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labour,” said Associate Professor Woodcock.

“We decided to look at the probability of a given string of letters being typed by a finite number of monkeys within a finite time period consistent with estimates for the lifespan of our universe,” he said.

The serious but light-hearted study, A numerical evaluation of the Finite Monkeys Theorem, has just been published in the peer-reviewed journal Franklin Open.

For number-crunching purposes, the researchers assumed that a keyboard contains 30 keys including all the letters of the English language plus common punctuation marks.

As well as a single monkey, they also did the calculations using the current global population of around 200,000 chimpanzees, and they assumed a rather productive typing speed of one key every second until the end of the universe in about 10^100 years — that’s a 1 followed by 100 zeros.

The results reveal that it is possible (around a 5% chance) for a single chimp to type the word ‘bananas’ in its own lifetime. However, even with all chimps enlisted, the Bard’s entire works (with around 884,647 words) will almost certainly never be typed before the universe ends.

“It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labour will ever be a viable tool for developing non-trivial written works,” the authors muse.

“This finding places the theorem among other probability puzzles and paradoxes — such as the St. Petersburg paradox, Zeno’s paradox, and the Ross-Littlewood paradox — where using the idea of infinite resources gives results that don’t match up with what we get when we consider the constraints of our universe,” said Associate Professor Woodcock.

In the era of generative AI, the Infinite Monkey Theorem, and its finite version, perhaps also challenge readers to consider philosophical questions around the nature of creativity, meaning and consciousness, and how these qualities emerge.

“We’re moving away from this anthropocentric view that ethanol is just something that humans use,” says behavioral ecologist and senior author Kimberley Hockings of the University of Exeter. “It’s much more abundant in the natural world than we previously thought, and most animals that eat sugary fruits are going to be exposed to some level of ethanol.”

Ethanol first became abundant around 100 million years ago, when flowering plants began producing sugary nectar and fruits that yeast could ferment. Now, it’s present naturally in nearly every ecosystem, though concentrations are higher, and production occurs year-round in lower-latitude and humid tropical environments compared to temperate regions. Most of the time, naturally fermented fruits only reach 1%-2% alcohol by volume (ABV), but concentrations as high as 10.2% ABV have been found in over-ripe palm fruit in Panama.

Animals already harbored genes that could degrade ethanol before yeasts began producing it, but there is evidence that evolution fine-tuned this ability for mammals and birds that consume fruit and nectar. In particular, primates and treeshrews have adapted to efficiently metabolize ethanol.

“From an ecological perspective, it is not advantageous to be inebriated as you’re climbing around in the trees or surrounded by predators at night — that’s a recipe for not having your genes passed on,” says molecular ecologist and senior author Matthew Carrigan of the College of Central Florida. “It’s the opposite of humans who want to get intoxicated but don’t really want the calories — from the non-human perspective, the animals want the calories but not the inebriation.”

It’s unclear whether animals intentionally consume ethanol for ethanol’s sake, and more research is needed to understand its impact on animal physiology and evolution. However, the researchers say that ethanol consumption could carry several benefits for wild animals. First and foremost, it’s a source of calories, and the odorous compounds produced during fermentation could guide animals to food sources, though the researchers say it’s unlikely that animals can detect ethanol itself. Ethanol could also have medicinal benefits: fruit flies intentionally lay their eggs in substances containing ethanol, which protects their eggs from parasites, and fruit fly larvae increase their ethanol intake when they become parasitized by wasps.

“On the cognitive side, ideas have been put forward that ethanol can trigger the endorphin and dopamine system, which leads to feelings of relaxation that could have benefits in terms of sociality,” says behavioral ecologist and first author Anna Bowland of the University of Exeter. “To test that, we’d really need to know if ethanol is producing a physiological response in the wild.”

There are a lot of unanswered questions regarding the significance of ethanol consumption to wild animals. In their future research, the team plans to investigate the behavioral and social implication of ethanol consumption in primates and to more deeply examine the enzymes involved in alcohol metabolism.

This research was supported by the Primate Society of Great Britain, the Wenner-Gren Foundation, the Canada Research Chairs program, and the Natural Sciences and Engineering Research Council of Canada.

In order to investigate whether and how nanoplastic particles in the body interact with antibiotics, the research team led by Lukas Kenner (MedUni Vienna), Barbara Kirchner (University of Bonn) and Oldamur Hollóczki (University of Debrecen) linked a common drug with widely used types of plastic. The focus was on the broad-spectrum antibiotic tetracycline, which is used to treat many bacterial infections, such as those of the respiratory tract, skin or intestines. When it came to plastics, the choice fell on polyethylene (PE), polypropylene (PP) and polystyrene (PS), which are ubiquitous components of packaging materials, as well as nylon 6,6 (N66), which is contained in many textiles such as clothing, carpets, sofa covers and curtains. Nanoplastics are smaller than 0.001millimeters and are considered particularly harmful to humans and the environment due to their small size.

Using complex computer models, the team was able to prove that the nanoplastic particles can bind tetracycline and thus impair the effectiveness of the antibiotic. “The binding was particularly strong with nylon,” emphasizes Lukas Kenner, pointing out a largely underestimated danger indoors: “The micro- and nanoplastic load is around five times higher there than outdoors. Nylon is one of the reasons for this: it is released from textiles and enters the body via respiration, for example.”

Danger of antibiotic resistance

As the study results show, the binding of tetracycline to nanoplastic particles can reduce the biological activity of the antibiotic. At the same time, binding to nanoplastics could lead to the antibiotic being transported to unintended sites in the body, causing it to lose its targeted effect and possibly cause other undesirable effects. “Our finding that the local concentration of antibiotics on the surface of the nanoplastic particles can increase is particularly worrying,” reports Lukas Kenner on another detail from the study. This increase in concentration could lead to the development of antibiotic-resistant bacteria. Plastics such as nylon 6,6, but also polystyrene, which bind more strongly to tetracycline, could therefore increase the risk of resistance. “At a time when antibiotic resistance is becoming an ever greater threat worldwide, such interactions must be taken into account,” says Kenner.

The study shows that exposure to nanoplastics is not only a direct health risk, but can also indirectly influence the treatment of diseases. “If nanoplastics reduce the effectiveness of antibiotics, the dosage poses a massive problem,” says Lukas Kenner with a view to future studies looking at the influence of nanoplastics on other drugs.

The new reactor design could be a part of the solution to the pressing problem of emission impacts on the climate and biosphere by enabling more agile and scalable carbon dioxide mitigation strategies.

A study in Nature Energy describes the specialized reactor as having a modular, three-chambered structure with a carefully engineered porous solid electrolyte layer at its core. Haotian Wang, a Rice chemical and biomolecular engineer whose lab has been researching industrial decarbonization and energy conversion and storage solutions, said the work “represents a big milestone in carbon capture from the atmosphere.”

“Our research findings present an opportunity to make carbon capture more cost-effective and practically viable across a wide range of industries,” said Wang, the corresponding author on the study and associate professor of chemical and biomolecular engineering.

The device has achieved industrially relevant rates of carbon dioxide regeneration from carbon-containing solutions. Its performance metrics, including its long-term stability and adaptability to different cathode and anode reactions, showcase its potential for wide-scale industrial use.

“One of the major draws of this technology is its flexibility,” said Wang, explaining that it works with different chemistries and can be used to cogenerate hydrogen. “Hydrogen coproduction during direct air capture could translate into dramatically lower capital and operation costs for downstream manufacturing of net-zero fuels or chemicals.”

The new technology offers an alternative to the use of high temperatures in direct air capture processes, which often involve running a mixed gas stream through high-pH liquids in order to filter out carbon dioxide, an acidic gas. This first step of the process ties up the carbon and oxygen atoms in the gas molecules to other compounds in the liquid, forming new bonds of varying degrees of strength depending on the type of chemical used to trap the carbon dioxide. The next major step in the process involves retrieving the carbon dioxide from these solutions, which can be done using either heat, chemical reactions or electrochemical processes.

Zhiwei Fang, a Rice postdoctoral researcher who is a study co-first author, said conventional direct air capture technologies tend to use high-temperature processes to regenerate carbon dioxide from sorbent, or the carbon dioxide-filtering agent.

“Our work focused on using electrical energy instead of thermal energy to regenerate carbon dioxide,” Fang said, adding that the approach has several additional benefits, including it works at room temperature, needs no additional chemicals and generates no unwanted byproducts.

The types of chemicals used to trap the carbon dioxide have different drawbacks and advantages. Amine-based sorbents are the most widely used, in part because they tend to form weaker bonds which means less energy is required to take the carbon dioxide back out of the solution. However, they are highly toxic and unstable. Even though basic water-based solutions using sorbents like sodium hydroxide and potassium hydroxide are a greener alternative, they require much higher temperatures to release the carbon dioxide back out.

“Our reactor can efficiently split carbonate and bicarbonate solutions, producing alkaline absorbent in one chamber and high-purity carbon dioxide in a separate chamber,” said Wang. “Our innovative approach optimizes electrical inputs to efficiently control ion movement and mass transfer, reducing energy barriers.”

Wang said he hopes the research will motivate more industries to pursue sustainable processes and fuel the momentum toward a net-zero future. He added that this and other projects in his lab over the years reflect Rice’s strategic focus on sustainable energy innovation.

“Rice is the place to be if you are passionate about sustainability and energy innovation,” Wang said.

Other authors on the study are former Rice postdoctoral researcher Xiao Zhang and Rice doctoral alumni and former postdoctoral scientists Peng Zhu and Yang Xia.

The research was supported by the Robert A. Welch Foundation (C-2051) and the David and Lucile Packard Foundation (2020-71371).

Utilizing cutting-edge machine learning and systems biology, researchers analyzed and correlated huge data sets from flies and humans to identify key metabolites that impact lifespan in both species.Results published online in Nature Communicationssuggest that one of the metabolites, threonine, may hold promise as a potential therapeutic for aging interventions.

“These results would not have been possible without this pioneering approach,” says Buck professor Pankaj Kapahi, PhD, senior author of the paper. “There is a lot of data sitting out there that is not being correlated between species. I think this approach could be a game-changer when it comes to identifying potential interventions to improve human health.”

Threonine has been shown to protect against diabetes in mice. The essential amino acid plays an important role in collagen and elastin production and is also involved in blood clotting, fat metabolism and immune function.

The method — simplified

The work began with former Buck postdoc Tyler Hilsabeck, PhD, crunching data (involving metabolomics, phenotypes and genomics) to analyze 120 metabolites in 160 strains of fruit flies on both restricted and normal diets. The goal was to reveal how different genotypes responded to the diets to influence lifespan and healthspan. “This allowed us to find the ‘needles in the haystack’ when it came to identifying relevant metabolites,” Hilsabeck says.

Vikram Narayan, PhD, a postdoctoral fellow then cross-referenced findings with human data from the massive UK Biobank. “Using the human data allowed us to focus on interesting metabolites to those that are conserved in both species. It also allowed us to uncover the impact of those metabolites in humans,” he says. Importantly, the team then brought those relevant metabolites back into the fly to validate results.

The results

In flies, threonine extended lifespan in a strain-and-sex-specific manner. Individuals with higher levels of threonine-related metabolites had longer, healthier lives. “We’re not saying that threonine is going to work in all conditions,” says Kapahi. “Our research shows it works in subsets of both flies and people. I think most of us have stopped expecting to find a ‘magic-bullet’ intervention for aging. Our method provides another way to develop precision medicine for geroscience.”

The results also include findings that were not so positive for both species. Orotate, which is relatively understudied and has been linked with fat metabolism, was negatively associated with aging. In flies orotate counteracted the positive impact of dietary restriction across every strain of the animals. In humans, orotate was linked to a shorter lifespan.

Larger implications

Kapahi hopes the larger research community will begin employing this method. “So many times we find things that work in worms and flies and then we don’t have the resources to move the basic science forward. This approach allows us to say with a lot more certainty that discoveries are going to be relevant in humans.” Kapahi says this method may reduce the need for studies in mice, something he welcomes.