It's a well known fact that most dogs have an amazing sense of smell, but just how do they use it? What do they do with it? And what's some of the math behind it?

To investigate this question we first took our "Math Loving Dog" Alpha to Toronto's own Scent Den at Wholesome Canine to see sniffing / smelling in action first hand!

How Dogs Use Smell

The first thing to know is that dogs use their sense of smell in many different ways. A dog will use their sense of smell to catalogue and map out where they have been and where things are; it's used to identify other dogs or animals that have been in that area; it's used to track objects or animals or even people; it's used to learn about new animals they meet and introduce themselves; and it's used to identify food and even determine if the food is safe to eat or not. A dog's sense of smell is vitally important to them.

A dog's sense of smell can also be important to humans as well, with some dogs being trained to find missing people, or to sniff out illegal substances or even explosives. They can also be trained to smell and identify various scents in food, plants and even some diseases in humans; and to compare them to one another and make matches of the same smells.¹

Some researchers¹ have also studied how dogs can use their sense of smell to track an object and have found that they know what object they expect to find (like having them track a ball but finding a piece of cloth at the end of the trail). When the dog found the object at the end of the trail (the cloth), and realized it wasn't what they expected to find (the ball), they continued to look for what they thought would be at the end (the ball).

This use of smell is even more powerful than their sense of sight, with dogs being able to sniff out objects in both full light and low/near-no light² with the same accuracy. Some dogs have been bred specifically to have a heightened sense of smell and studies have shown that some dogs have at least a 100 times greater sense of smell than humans for certain scents² (and humans can smell over 10,000 different things)⁵.

Dogs can even use their sniffers to tell time³, the idea being that strong smells are newer and weak smells are older. So when you leave your pup alone your scent starts off strong and gets weaker the longer you are away. This gives the dog a sense of how long you've been gone. If you leave and come back the same time every day then they can tell time (in a way) by how weak your scent is and know that when it reaches a certain level, you'll be back!

How Do Smells Work?

The air around us is filled with millions of tiny molecules that make up the air we breath. Surprisingly the air we breath is made up mostly of nitrogen (78%) with only 21% being oxygen (what we need to breath in to live) and less than 0.1% carbon dioxide (what we breath out). The rest is made up of Argon (0.9%) and other trace gases.

All of these gases are floating around making up the air we breath. To smell we pull this air through our noses across many different olfactory receptors, which then send a signal to our brain (kind of like the eyes take in light through receptors in the eyes and the brain processes what is being seen).

Let's pretend we have a rotten egg. When we first crack open the egg there is no immediate smell, but after a second the gases that were trapped inside that egg float up and meet our noses. Once these gases go over our olfactory senses we process the smell of rotten egg in our brain (yuck!). Now, being close to the source of the smell, at the time it occurs, means we smell it very strongly.

A few minutes later, someone a few rooms over from us starts to gag a little and asks "what is that horrible smell?" This is because the gases from the rotten egg have diffused, or spread, through the air in the house, using wind patterns in the house (from an open window or a fan blowing air). The smell the second person experiences will be less intense than ours because the smell has spread out, the gases didn't stay in a clump like they did for us when they escaped the egg (lucky us), but the other person's sniffer is sensitive enough to know that we just broke open a rotten egg.

So... Math?

Math comes in really handy here to help us explain a number of concepts associated with smelling (and to explain how dogs use smell).

Telling Time: when you first leave the house your smell for the dog is the strongest. As time passes your smell diffuses around the house, escapes through open windows or cracks (no house is perfectly airtight) and becomes less and less. A dog can use this lessened smell strength to calculate how long you've been gone based on how weak your remaining smell is. They are essentially calculating the strength of the smell when you first left minus how much weaker the smell has gotten to determine how much time has passed.

Mapping Locations and Communicating: Many dogs will use smells to create a mental map of their neighbourhood and who lives there. Dogs often use urine to mark their location as a way to both communicate to other dogs that they were there (kind of like doggy pee-mail) and also to leave themselves a trail to follow to get back home. Human surveyors and map makers will use similar methods to make their maps by using markers and drawing detailed plans to follow. While humans might not use smells to do this both dogs and human surveyors use a system of markers to make their maps.

Many dogs will use smells to create a mental map of their neighbourhood and who lives there. Dogs often use urine to mark their location as a way to both communicate to other dogs that they were there (kind of like doggy pee-mail) and also to leave themselves a trail to follow to get back home. Human surveyors and map makers will use similar methods to make their maps by using markers and drawing detailed plans to follow. While humans might not use smells to do this both dogs and human surveyors use a system of markers to make their maps.

Many dogs will use smells to create a mental map of their neighbourhood and who lives there. Dogs often use urine to mark their location as a way to both communicate to other dogs that they were there (kind of like doggy pee-mail) and also to leave themselves a trail to follow to get back home. Human surveyors and map makers will use similar methods to make their maps by using markers and drawing detailed plans to follow. While humans might not use smells to do this both dogs and human surveyors use a system of markers to make their maps.

Finding Things: Similar to mapping dogs will use scent to determine if they are getting closer to an object or farther away, the stronger the smell, the closer they are (and weaker means farther away). It's kind of like when people play hot and cold (close your eyes and someone says you're getting hotter - closer - to an object or colder - farther away). Dogs can calculate the direction they should be going based on the smell.

While dogs don't use equations or numbers directly they do use a number of different math skills for sniffing: critical thinking skills, logic skills and mapping techniques. And humans use math equations and skills when calculating diffusion rates of gases (useful for understanding how chemical spills will spread and if homes have to be evacuated based on wind or air patterns) or using graphing skills to create maps of locations.

So, What Do We Know?

We know that dogs use their sense of smell for many different uses and that their sense of smell is far superior to humans.

We also know that dogs and humans use math skills related to smelling to navigate the world around them and communicate with one another.

Finally, we know that smells travel through the air through diffusion and studying this has a number of real world applications.

Try it Yourself

Here are some experiments you try at home...

• Take a perfume or scented oil (hopefully a pleasant one) and put a drop of a piece of paper or a Kleenex, go into another room and start a timer to see how long it takes before the smell moves to the room you're in. Try it with different scents and see if the time is different.
• Put a smell in a room and then leave the room, come back every 20 - 30 minutes and see if you can still smell it? Is the smell weaker each time you come back? How long until it goes away? Note: you may need to go outside and come back in for this one to work as humans are able to unconsciously ignore smells after a while.
• Humans have better eyes, and cognitive skills, than dogs. Try using those to make a map of an area you're not sure of by using place markers (like a small flag or toy or sticker) to mark notable locations (like a tree if you can do this outside) and then draw a map of the area using your markers. For an added challenge use a measuring tape / ruler to make accurate measurements between your markers and build as detailed of a map that you can.

Our Thanks

We'd like to extend our sincere thanks to the Scent Den for a wonderful experience where Alpha was able to try out all sorts of sniffing skills to learn more about his environment, map it out and discover all the scrumptious treats hidden throughout. You can learn more about the Scent Den in the BlogTO article or on Wholesome Canines website Please note: we are in no way affiliated with Wholesome Canine or are paid to endorse their products, we just really enjoyed our time there!

References

(1) Bräuer, J., & Belger, J. (2018). A ball is not a Kong: Odor representation and search behavior in domestic dogs (Canis familiaris) of different education. Journal of Comparative Psychology, 132(2), 189–199. https://doi.org/10.1037/com0000115
(2) Gazit, I., & Terkel, J. (2003). Domination of olfaction over vision in explosives detection by dogs. Applied Animal Behaviour Science, 82(1), 65–73. https://doi.org/10.1016/S0168-1591(03)00051-0
(3) Can Dogs Tell Time? (2016, October 12). Retrieved April 29, 2019, from Animal Cognition website: http://www.animalcognition.org/2016/10/12/can-dogs-tell-time/
(4) Percentage of Nitrogen in the Air. (n.d.). Retrieved April 30, 2019, from Sciencing website: https://sciencing.com/percentage-nitrogen-air-5704002.html
(5) Binns, C. (n.d.). How We Smell. Retrieved April 30, 2019, from Live Science website: https://www.livescience.com/10457-smell.html