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How do mammals estimate the speed of moving objects?

How do mammals estimate the speed of moving objects?



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Has there been any research on how mammals predict the speed of moving objects? In particular, how do they integrate top-down information? For instance, do they have greater difficulty estimating the speed of a fast-moving sloth more than a moving mouse?


Two areas in the visual cortex are associated with the perception of velocity, namely:

  1. The primary visual cortex (V1) and
  2. The middle temporal area (MT or V5).

Both V1 and MT contain neurons that respond strongly to motion in a particular direction and also have selective responses to a particular speed. Direction and speed together define the velocity vector, i.e., these V1 and MT neurons are velocity-tuned. The velocity tuned neurons in V1 typically project to velocity tuned cells in MT. While V1 contains approximately 25% velocity-tuned neurons, those in the MT neurons are nearly all velocity-tuned (Bradley & Goyal, 2008).

Now this is all bottom-up processing. You basically ask as well whether top-down issues play a role. I do not think so. The visual system is basically split in a dorsal 'what' and a ventral 'where' stream (Fig. 1). The 'what' system identifies a target and the 'where' system (containing MT) determines location and velocity. As far as I know, there is no feedback from the dorsal stream onto the ventral one to affect velocity processing.


Fig. 1. Dorsal (parietal) and ventral (temporal) streams. source: Lehky & Sereno (2007)

References
- Bradley & Goyal, &Nature Rev Neurosci (2008); 9: 686-95
- Lehky & Sereno, *J Neurophysiol (2007); 97(1): 307-19


@AliceD gave a great answer on the bottom up pathway. Let me add some top-down processing bits into the picture, since that's what you are asking.

First of all, at a perceptual level, motion perception is biased by prior expectations and strength of motion signal. E.g., see:

  • Stocker, A. A. and Simoncelli, E. P. (2006). Noise characteristics and prior expectations in human visual speed perception. Nature Neuroscience, 9(4):578-585. http://dx.doi.org/10.1038/nn1669

The neural activity of MT (and behavior) is known to be modulated by attention. E.g., see:

  • Monkey Area MT Latencies to Speed Changes Depend on Attention and Correlate with Behavioral Reaction Times. Neuron. 78(4):740-750. http://doi.org/10.1016/j.neuron.2013.03.014

Syntax

Description

opticFlow = opticalFlowLK returns an optical flow object that you can use to estimate the direction and speed of the moving objects in a video. The optical flow is estimated using the Lucas-Kanade method.

opticFlow = opticalFlowLK( 'NoiseThreshold' , threshold ) returns an optical flow object with the property 'NoiseThreshold' specified as a Name,Value pair. Enclose the property name in quotes.

For example, opticalFlowLK('NoiseThreshold',0.05)


Artificial ‘brain’ reveals why we can’t always believe our eyes

A computer network closely modelled on part of the human brain is enabling new insights into the way our brains process moving images - and explains some perplexing optical illusions.

It’s very hard to directly measure what’s going on inside the human brain when we perceive motion - even our best medical technology can’t show us the entire system at work. With MotionNet we have complete access.

Reuben Rideaux

By using decades’ worth of data from human motion perception studies, researchers have trained an artificial neural network to estimate the speed and direction of image sequences.

The new system, called MotionNet, is designed to closely match the motion-processing structures inside a human brain. This has allowed the researchers to explore features of human visual processing that cannot be directly measured in the brain.

Their study, published today in the Journal of Vision, uses the artificial system to describe how space and time information is combined in our brain to produce our perceptions, or misperceptions, of moving images.

The brain can be easily fooled. For instance, if there’s a black spot on the left of a screen, which fades while a black spot appears on the right, we will ‘see’ the spot moving from left to right – this is called ‘phi’ motion. But if the spot that appears on the right is white on a dark background, we ‘see’ the spot moving from right to left, in what is known as ‘reverse-phi’ motion.”

The researchers reproduced reverse-phi motion in the MotionNet system, and found that it made the same mistakes in perception as a human brain – but unlike with a human brain, they could look closely at the artificial system to see why this was happening. They found that neurons are ‘tuned’ to the direction of movement, and in MotionNet, ‘reverse-phi’ was triggering neurons tuned to the direction opposite to the actual movement.

The artificial system also revealed new information about this common illusion: the speed of reverse-phi motion is affected by how far apart the dots are, in the reverse to what would be expected. Dots ‘moving’ at a constant speed appear to move faster if spaced a short distance apart, and more slowly if spaced a longer distance apart.

“We’ve known about reverse-phi motion for a long time, but the new model generated a completely new prediction about how we experience it, which no-one has ever looked at or tested before,” said Dr Reuben Rideaux, a researcher in the University of Cambridge’s Department of Psychology and first author of the study.

Humans are reasonably good at working out the speed and direction of a moving object just by looking at it. It’s how we can catch a ball, estimate depth, or decide if it’s safe to cross the road. We do this by processing the changing patterns of light into a perception of motion – but many aspects of how this happens are still not understood.

“It’s very hard to directly measure what’s going on inside the human brain when we perceive motion - even our best medical technology can’t show us the entire system at work. With MotionNet we have complete access,” said Rideaux.

Thinking things are moving at a different speed than they really are can sometimes have catastrophic consequences. For example, people tend to underestimate how fast they are driving in foggy conditions, because dimmer scenery appears to be moving past more slowly than it really is. The researchers showed in a previous study that neurons in our brain are biased towards slow speeds, so when visibility is low they tend to guess that objects are moving more slowly than they actually are.

Revealing more about the reverse-phi illusion is just one example of the way that MotionNet is providing new insights into how we perceive motion. With confidence that the artificial system is solving visual problems in a very similar way to human brains, the researchers hope to fill in many gaps in current understanding of how this part of our brain works.

Predictions from MotionNet will need to be validated in biological experiments, but the researchers say that knowing which part of the brain to focus on will save a lot of time.

Rideaux and his study co-author Dr Andrew Welchman are part of Cambridge’s Adaptive Brain Lab, where a team of researchers is examining the brain mechanisms underlying our ability to perceive the structure of the world around us.

This research was supported by the Leverhulme Trust and the Isaac Newton Trust.

/>
The text in this work is licensed under a Creative Commons Attribution 4.0 International License. Images, including our videos, are Copyright ©University of Cambridge and licensors/contributors as identified. All rights reserved. We make our image and video content available in a number of ways – as here, on our main website under its Terms and conditions, and on a range of channels including social media that permit your use and sharing of our content under their respective Terms.


How to Calculate Momentum

We will define the concept of momentum in the context of physics and use the mathematics of vectors and differences (such as the difference in time, Δt) to derive the law of conservation of linear momentum and to apply it to various problems.

o Law of conservation of linear momentum

o Understand the physical definition of momentum

o Derive the law of conservation of linear momentum

o Apply this conservation law to solving problems involving linear motion

We have used the concepts of mass and velocity to describe the motion of objects. Imagine two objects, one with a small mass and one with a large mass consider, for instance, a tennis ball (less massive) and a medicine ball (more massive). Now, imagine the two objects being thrown at you at some speed v obviously, getting hit by a tennis ball traveling at speed v sounds much less painful than getting hit by a medicine ball traveling at speed v. Consider also the medicine ball traveling at two different speeds: a slower speed, s, and a faster speed, f. Trying to catch a medicine ball traveling at speed s (the slower speed) certainly sounds easier than trying to catch one traveling at a faster speed f! We tend to think of a larger object traveling at a particular speed as having more momentum than a smaller object traveling at that speed. Likewise, we think of one object traveling at a fast speed as having more momentum than that object traveling at a lower speed. Momentum, therefore, increases with increasing speed as well as increasing mass. This situation fits logically, then, with the definition of momentum in physics. The momentum p of an object of mass m and velocity v is defined according to the following relationship:

p = mv

Notice that momentum, like velocity, is a vector with both magnitude and direction. As the mass or velocity of an object increase, so does the momentum.

The Relationship Between Momentum and Force

Recall that acceleration is simply the time rate of change of velocity. Thus (on average), we can write the following:

Let's substitute this into our force expression from Newton's second law of motion:

Assuming the mass m remains constant, we can make the following change:

Note that because mv appears in the net force expression, we can write it in terms of momentum p. The net force on an object is therefore the time rate of change of its momentum.

Practice Problem: A 50-kilogram object is moving at a speed of 10 meters per second. What is its momentum?

Solution: The momentum, p, of the object is simply the product of its mass and its velocity: p = mv. Because no direction is specified, we are only interested in determining the magnitude of p, or p. Thus,

Note the units in the result--we can also express the units in terms of newton seconds.

Let's now consider some arbitrary number of objects the total momentum P of the system of objects is simply the sum of all the individual momenta: . In the same manner, following Newton's second law, we'll call Ftot the sum of all the forces acting on the objects. But this sum, Ftot, is simply the sum of all external forces acting on the system of objects. Then,

And if no external forces are acting on the system of objects,

In other words, the time rate of change of the total momentum of the system of objects is zero in this case this is simply a statement of the law of conservation of linear momentum for a closed and isolated system. That is to say, the total momentum is constant for a given system of objects on which no external force acts. This conclusion is extremely useful for problems involving, for instance, collisions of objects. The following practice problems allow you to explore the implications of this result.

Practice Problem: A projectile of mass 1 kilogram traveling at 80 meters per second collides head on with another projectile of mass 2 kilograms traveling at 60 meters per second in the opposite direction. If the projectiles "stick" together after their collision, what is their velocity after colliding?

Solution: Let's draw a diagram of the situation before and after the collision. We also define the direction x for reference.

From the lesson we learned that the total linear momentum of a system of objects must be conserved (that is, unchanged) if no external forces act on that system. In this case, it is assumed that no forces outside the system act upon the two objects. The total momentum before the collision must therefore be the same as the total momentum after the collision. Let's first calculate the total momentum before the collision (Pi):

After the collision, because the two objects "stick" together, they effectively become a single object with a mass of 3 kg and some velocity v. The momentum of this object, Pf, is

We want to calculate v, which is the velocity of the objects after collision. Because the momentum before the collision is the same as that after,

Thus, the velocity of the objects after collision is 13.3 meters per second in the same direction as that of the larger object before the collision (which we have defined here as the negative x direction).

Practice Problem: An astronaut with all his equipment and tools has a mass of 125 kilograms. An accident occurs in space, causing him to become detached from a space station and to drift into space at a speed of one meter per second. One of his tools weighs five kilograms, and decides to use it to get back to the station. If he throws the tool directly away from the station, what is the minimum speed at which he must throw it to get himself moving back toward the station?

Solution: As usual, we can greatly assist the problem-solving process by drawing a diagram of the situation. The diagram need not be artistic--simple figures are often sufficient for representing different objects.

Part of the astronaut's weight is a five-kilogram tool if he throws this away from himself (and also directly away from the station) with sufficient velocity, he can (by conservation of momentum) cause himself to begin moving back toward the station. This situation is illustrated below. Note that the mass of the astronaut decreases by five kilograms when he throws the tool away.

We can use the law of conservation of momentum to calculate the speed at which the astronaut must throw the tool to reverse his alarming course and send him back toward the station. The initial total momentum of the astronaut, Pi, is the following. We'll define as x the direction away from the station.

This must also be the total momentum of the astronaut and the tool after he throws it away--we'll call this final momentum Pf. Let's calculate the speed of the tool required to bring the astronaut to a stop any speed above this number will cause the astronaut to move toward the station.


Unconscious Perception

We encounter more stimuli than we can attend to unconscious perception helps the brain process all stimuli, not just those we take in consciously.

Learning Objectives

Describe the relationship between priming and subliminal stimulation

Key Takeaways

Key Points

  • Unconscious perception involves the processing of sensory inputs that have not been selected for conscious perception.
  • Unconsciously, the brain processes all the stimuli we encounter, not just those we consciously attend to. The brain takes in these signals and interprets them in ways that influence how we respond to our environment.
  • Priming is an unconscious process whereby neural networks are activated and strengthened, which influences perception of future stimuli.
  • Priming allows for the brain to quickly and efficiently process stimuli from the environment.

Key Terms

  • stimulus: In psychology, any energy pattern (e.g., light or sound) that is registered by the senses.
  • priming: The implicit memory effect in which exposure to a stimulus influences response to a subsequent stimulus.
  • Perception: The organization, identification, and interpretation of sensory information.

Individuals take in more stimuli from their environment than they can consciously attend to at any given moment. The brain is constantly processing all the stimuli it is exposed to, not just those that it consciously attends to. Unconscious perception involves the processing of sensory inputs that are not selected for conscious perception. The brain takes in these unnoticed signals and interprets them in ways that influence how individuals respond to their environment.

Priming

The perceptual learning of unconscious processing occurs through priming. Priming occurs when an unconscious response to an initial stimulus affects responses to future stimuli. One of the classic examples is word recognition, thanks to some of the earliest experiments on priming in the early 1970s: the work of David Meyer and Roger Schvaneveldt showed that people decided that a string of letters was a word when the letters followed an associatively or semantically related word. For example, NURSE was recognized more quickly when it followed DOCTOR than when it followed BREAD. This is one of the simplest examples of priming. When information from an initial stimulus enters the brain, neural pathways associated with that stimulus are activated, and a second stimulus is interpreted through that specific context.

Experience affects the activation of neural networks: When information from an initial stimulus enters the brain, neural pathways associated with that stimulus are activated, and the stimulus is interpreted in a specific manner.

One example of priming is in the childhood game Simon Says. Simon is able to trick the players because of priming. By saying “Simon says touch your nose,” “Simon says touch your ear,” and so on, participants are primed to follow the “Simon says” direction and are likely to slip up when that phrase is omitted because they expect it to be there.

In another example, individuals in a study were primed with neutral, polite, or rude words prior to an interview with an investigator. Priming the participants with words prior to the interview activated the neural circuits associated with reactions to those words. The participants who had been primed with rude words interrupted the investigator most often, and those primed with polite words did so the least often.

Subliminal Stimulation

The presentation of an unattended stimulus can prime our brains for a future response to that stimulus. This process is known as subliminal stimulation. A number of studies have examined how unconscious stimuli influence human perception. Researchers, for example, have demonstrated how the type of music that is played in supermarkets can influence the buying habits of consumers. In another study, researchers discovered that holding a cold or hot beverage prior to an interview can influence how the individual perceives the interviewer. While subliminal stimulation appears to have a temporary effect, there is no evidence yet that it produces an enduring effect on behavior.


Artificial ‘brain’ reveals why we can’t always believe our eyes

A computer network closely modelled on part of the human brain is enabling new insights into the way our brains process moving images - and explains some perplexing optical illusions.

It’s very hard to directly measure what’s going on inside the human brain when we perceive motion - even our best medical technology can’t show us the entire system at work. With MotionNet we have complete access.

Reuben Rideaux

By using decades’ worth of data from human motion perception studies, researchers have trained an artificial neural network to estimate the speed and direction of image sequences.

The new system, called MotionNet, is designed to closely match the motion-processing structures inside a human brain. This has allowed the researchers to explore features of human visual processing that cannot be directly measured in the brain.

Their study, published today in the Journal of Vision, uses the artificial system to describe how space and time information is combined in our brain to produce our perceptions, or misperceptions, of moving images.

The brain can be easily fooled. For instance, if there’s a black spot on the left of a screen, which fades while a black spot appears on the right, we will ‘see’ the spot moving from left to right – this is called ‘phi’ motion. But if the spot that appears on the right is white on a dark background, we ‘see’ the spot moving from right to left, in what is known as ‘reverse-phi’ motion.”

The researchers reproduced reverse-phi motion in the MotionNet system, and found that it made the same mistakes in perception as a human brain – but unlike with a human brain, they could look closely at the artificial system to see why this was happening. They found that neurons are ‘tuned’ to the direction of movement, and in MotionNet, ‘reverse-phi’ was triggering neurons tuned to the direction opposite to the actual movement.

The artificial system also revealed new information about this common illusion: the speed of reverse-phi motion is affected by how far apart the dots are, in the reverse to what would be expected. Dots ‘moving’ at a constant speed appear to move faster if spaced a short distance apart, and more slowly if spaced a longer distance apart.

“We’ve known about reverse-phi motion for a long time, but the new model generated a completely new prediction about how we experience it, which no-one has ever looked at or tested before,” said Dr Reuben Rideaux, a researcher in the University of Cambridge’s Department of Psychology and first author of the study.

Humans are reasonably good at working out the speed and direction of a moving object just by looking at it. It’s how we can catch a ball, estimate depth, or decide if it’s safe to cross the road. We do this by processing the changing patterns of light into a perception of motion – but many aspects of how this happens are still not understood.

“It’s very hard to directly measure what’s going on inside the human brain when we perceive motion - even our best medical technology can’t show us the entire system at work. With MotionNet we have complete access,” said Rideaux.

Thinking things are moving at a different speed than they really are can sometimes have catastrophic consequences. For example, people tend to underestimate how fast they are driving in foggy conditions, because dimmer scenery appears to be moving past more slowly than it really is. The researchers showed in a previous study that neurons in our brain are biased towards slow speeds, so when visibility is low they tend to guess that objects are moving more slowly than they actually are.

Revealing more about the reverse-phi illusion is just one example of the way that MotionNet is providing new insights into how we perceive motion. With confidence that the artificial system is solving visual problems in a very similar way to human brains, the researchers hope to fill in many gaps in current understanding of how this part of our brain works.

Predictions from MotionNet will need to be validated in biological experiments, but the researchers say that knowing which part of the brain to focus on will save a lot of time.

Rideaux and his study co-author Dr Andrew Welchman are part of Cambridge’s Adaptive Brain Lab, where a team of researchers is examining the brain mechanisms underlying our ability to perceive the structure of the world around us.

This research was supported by the Leverhulme Trust and the Isaac Newton Trust.

/>
The text in this work is licensed under a Creative Commons Attribution 4.0 International License. Images, including our videos, are Copyright ©University of Cambridge and licensors/contributors as identified. All rights reserved. We make our image and video content available in a number of ways – as here, on our main website under its Terms and conditions, and on a range of channels including social media that permit your use and sharing of our content under their respective Terms.


Syntax

Description

opticFlow = opticalFlowLK returns an optical flow object that you can use to estimate the direction and speed of the moving objects in a video. The optical flow is estimated using the Lucas-Kanade method.

opticFlow = opticalFlowLK( 'NoiseThreshold' , threshold ) returns an optical flow object with the property 'NoiseThreshold' specified as a Name,Value pair. Enclose the property name in quotes.

For example, opticalFlowLK('NoiseThreshold',0.05)


56 thoughts on &ldquo No, It’s Not Just You: Why time “speeds up” as we get older &rdquo

I am 64 years old and have noticed how time seems to be flying by. As a result, I have spent a lot of time thinking about this. I believe a good part of this has to do with perception. If my life span was 250 years long, I do not think that time would appear to be flying by.

That’s one of the reasons I never accept the theory that we are the some total of our experience, the Doctor is convinced humans are biologic computers and being human is much more than that! For instance all life down to the smallest virus contain information stored in the DNA, Doctor!

It’s a relative thing. Einstein theory. As we get older each year is a small er part of our life. When I was 10 each year was 1 tenth of my life. I’m now 67 each year 1 67th of my life

This is my opinion as well. It makes the most sense and I feel age relative to it’s perportion of my life.

It is because….time is running out, unlike when we were all 14 and had unlimited time.
Now our minutes are nearly used up, and as Warren Zevon said,
“my sh*t is f*cked up.”

All i want to say that my elementary school lasted forever, as well as days in a high school. Times began to fly when in a college.

Why does time goes faster as we get older? That’s a crazy idea.

Guys, let’s be real. Ultimately there’s no such thing as a time machine. In other words, it is what it is. Time is goin by quick because we wasting time thinking about why time goes by quick. Live in the moment, it’s yours. In the meantime, take me back to Love Machine.


How Big Is the Universe?

If you've ever dreamed of time traveling, just look out at the night sky the glimmers you see are really snapshots of the distant past. That's because those stars, planets and galaxies are so far away that the light from even the closest ones can take tens of thousands of years to reach Earth.

The universe is undoubtedly a big place. But just how big is it?

"That may be something that we actually never know," Sarah Gallagher, an astrophysicist at Western University in Ontario, Canada, told Live Science. The size of the universe is one of the fundamental questions of astrophysics. It also might be impossible to answer. But that doesn't stop scientists from trying.

The closer an object is in the universe, the easier its distance is to measure, Gallagher said. The sun? Piece of cake. The moon? Even easier. All scientists have to do is shine a beam of light upward and measure the amount of time it takes for that beam to bounce off the moon's surface and back down to Earth.

But the most distant objects in our galaxy are trickier, Gallagher said. After all, reaching them would take a very strong beam of light. And even if we had the technological capabilities to shine a light that far, who has thousands of years to wait around for the beam to bounce off the universe's distant exoplanets and return back to us?

Scientists have a few tricks up their sleeves for dealing with the farthest objects in the universe. Stars change color as they age, and based on that color, scientists can estimate how much energy, and light, those stars give off. Two stars that have the same energy and brightness aren't going to appear the same from Earth if one of those stars is much farther away. The farther one will naturally appear dimmer. Scientists can compare a star's actual brightness with what we see from Earth and use that difference to calculate how far away the star is, Gallagher said.

But what about the absolute edge of the universe? How do scientists calculate distances to objects that far away? That's where things get really tricky.

Remember: the farther an object is from Earth, the longer the light from that object takes to reach us. Imagine that some of those objects are so far away that their light has taken millions or even billions of years to reach us. Now, imagine that some objects' light takes so long to make that journey that in all the billions of years of the universe, it still hasn't reached Earth. That's exactly the problem that astronomers face, Will Kinney, a physicist at the State University of New York at Buffalo, told Live Science.

"We can only see a tiny, little bubble of [the universe]. And what's outside of that? We don't really know," Kinney said.

But by calculating the size of that little bubble, scientists can estimate what's outside of it.

Scientists know that the universe is 13.8 billion years old, give or take a few hundred million years. That means that an object whose light has taken 13.8 billion years to reach us should be the very farthest object we can see. You might be tempted to think that gives us an easy answer for the size of the universe: 13.8 billion light-years. But keep in mind that the universe is also continuously expanding at an increasing rate. In the amount of time that light has taken to reach us, the edge of the bubble has moved. Luckily, scientists know just how far it's moved: 46.5 billion light-years away, based on calculations of universe&rsquos expansion since the big bang.

Some scientists have used that number to try and calculate what lies beyond the limit of what we can see. Based on the assumption that the universe has a curved shape, astronomers can look at the patterns we see in the observable universe and use models to estimate how much farther the rest of the universe extends. One study found that the actual universe could be at least 250 times the size of the 46.5 billion light-years we can actually see.

But Kinney has other ideas: "There's no evidence that the universe is finite," he said, "It might very well go on forever."

There's no saying for sure whether the universe is finite or infinite, but scientists agree that its "really freaking huge," Gallagher said. Unfortunately, the little part we can see now is the most we'll ever be able to observe. Because the universe is expanding at an increasing rate, the outer edges of our observable universe are actually moving outward faster than the speed of light. That means that our universe's edges are moving away from us faster than their light can reach us. Gradually, these edges (and any restaurants there, as British author Douglas Adams once wrote) are disappearing from view.

The universe's size, and the sheer amount of it that we can't see &mdash that's humbling, Gallagher said. But that doesn't stop her and other scientists from continuing to probe for answers.

"Maybe we won't be able to figure it out. It could be seen as frustrating," Gallagher said. "But it also makes it really exciting."


The outfielder problem: The psychology behind catching fly balls [Cognitive Daily]

It's football season in America: The NFL playoffs are about to start, and tonight, the elected / computer-ranked top college team will be determined. What better time than now to think about . baseball! Baseball players, unlike most football players, must solve one of the most complicated perceptual puzzles in sports: how to predict the path of a moving target obeying the laws of physics, and move to intercept it.

The question of how a baseball player knows where to run in order to catch a fly ball has baffled psychologists for decades. (You might argue that a football receiver faces a similar task, but generally in football, the distances involved are much shorter, and most football players aren't expected to catch passes at all.)

There are three primary possible explanations for how a baseball fielder catches a fly ball:

  • Trajectory Projection (TP): The fielder calculates the trajectory of a ball the moment it is hit and simply runs to the spot where it will fall (of course, taking into account wind speed and barometric pressure).
  • Optical acceleration cancellation (OAC): The fielder watches the flight of the ball constantly adjusting her position in response to what she sees. If it appears to be accelerating upward, she moves back. If it seems to be accelerating downward, she moves forward.
  • Linear optical trajectory (LOT): The fielder pays attention to the apparent angle formed by the ball, the point on the ground beneath the ball, and home plate, moving to keep this angle constant until she reaches the ball. In other words, she tries to move so that the ball appears to be moving in a straight line rather than a parabola.

In principle, all three of these systems should work. However, TP is probably impossible our visual system isn't accurate at determining distances beyond about 30 meters, and outfielders stand up to 100 meters away from home plate. The second system, OAC, might not work because the visual system isn't actually very sensitive to acceleration. And the third system, LOT, is problematic because it doesn't predict a unique path for the fielder to take to the ball. Further, the most likely paths a fielder would take to catch a ball wouldn't be much different under OAC and LOT.

But Philip Fink, Patrick Foo, and William Warren figured out a way to experimentally distinguish between all three models. They had 8 skilled male baseball players and 4 skilled female softball players don VR headsets and attempt to catch virtual balls in a large room. The room was big enough that they could freely move 6 meters in each direction. VR was necessary because the researchers made their virtual balls take paths that aren't possible in real life:

The players stood about 35 meters from "home plate" and the balls were hit either 4 meters in front or behind them. They were also offset to either side, but this turned out not to matter for the results. Here's a movie (QuickTime required) showing what a typical player saw in her VR display. And here's a movie showing what the players actually did.

As the image above shows, half the time the balls took their normal trajectory, but half the time they proceeded in a physically-impossible straight line for the second half of their flight. For the TP model, this shouldn't matter -- players should go straight to the landing point in either case. But with a straight-line motion, OAC and LOT predict very different paths. This graph compares one player's actual movements with the OAC model's projections:

The thick lines show the predicted movement if the player was following the OAC model, and the thin lines show the actual movement (tan[alpha] is the acceleration in the change of the angle of the ball relative to the player). As you can see, these patterns match up pretty well. But take a look at this graph:

Here, the thick lines show the predicted movement if the player was following LOT, and the thin lines show the actual movement (again, tan[alpha] is the acceleration in the change of the angle of the ball relative to the player, and tan[beta] is the acceleration in the angle between the ball's position above the ground and home plate). This time, the model does significantly worse after the ball shifts to a straight trajectory.

The researchers say this is compelling evidence that ball players do rely on the apparent acceleration of the ball's movement (OAC) in order to track it down and catch it. You'll notice from the second movie that the player clearly isn't moving in a straight line to catch the ball, so the TP model is also ruled out. Even though people aren't very good at detecting acceleration, apparently we're good enough to catch a fly ball hit 30 to 40 meters (and baseball players routinely shag fly balls hit over 100 meters!).


First-order motion perception refers to the perception of the motion of an object that differs in luminance from its background, such as a black bug crawling across a white page. This sort of motion can be detected by a relatively simple motion sensor designed to detect a change in luminance at one point on the retina and correlate it with a change in luminance at a neighbouring point on the retina after a delay. Sensors that work this way have been referred to as Reichardt detectors (after the scientist W. Reichardt, who first modelled them), Α] motion-energy sensors, Β] or Elaborated Reichardt Detectors. Γ] These sensors detect motion by spatio-temporal correlation and are plausible models for how the visual system may detect motion. Debate still rages about the exact nature of this process. First-order motion sensors suffer from the aperture problem, which means that they can detect motion only perpendicular to the orientation of the contour that is moving. Further processing is required to disambiguate true global motion direction.

Second-order motion is motion in which the moving contour is defined by contrast, texture, flicker or some other quality that does not result in an increase in luminance or motion energy in the Fourier spectrum of the stimulus. Δ] Ε] There is much evidence to suggest that early processing of first- and second-order motion is carried out by separate pathways. Ζ] Second-order mechanisms have poorer temporal resolution and are low-pass in terms of the range of spatial frequencies that they respond to. Second-order motion produces a weaker motion aftereffect unless tested with dynamically flickering stimuli. Η] First and second-order signals appear to be fully combined at the level of Area V5/MT of the visual system.


Who’s (sort of) counting?

Symbolic numbers work well for people. For millions of years, however, other animals without full powers to count have managed life-and-death decisions about magnitude (which fruit pile to grab, which fish school to join, whether there are so many wolves that it’s time to run).

ORIENTAL FIRE-BELLIED TOAD Bombina orientalis is one of the few amphibians that has been tested for number sense. Test animals showed more interest in eight yummy mealworms than four. That was true when treats were the same size. A visual shortcut like surface area may make more of a difference than numerosity.
Source: G. Stancher et al/Anim. Cogn. 2015 Vassil/Wikimedia Commons ORANGUTAN Much of the research on nonhuman number sense involves primates. A zoo orangutan that was trained to use a touch screen was able to pick which of two arrays had the same number of dots, shapes or animals shown in a previous sample.
Source: J. Vonk/Anim. Cogn. 2014 m_ewell_young/iNaturalist.org (CC BY-NC 4.0) CUTTLEFISH The first test of number sense in Sepia pharaonis, published in 2016, reports that cuttlefish typically move to eat a quartet of shrimp rather than a threesome, even when the three shrimp are crowded around so the density is the same as in the quartet.
Source: T.-I. Yang and C.-C. Chiao/Proc. R. Soc. B 2016 Stickpen/Wikimedia Commons HONEYBEE Honeybees that had learned to tell two dots from three did pretty well when tested with dots of different colors, oddly positioned among distracting shapes or even when replaced with yellow stars.
Source: Gross et al/PLOS ONE 2009 Keith McDuffee/Flickr (CC BY 2.0) HORSE Horses have a special sad place in the history of number studies. That’s because a famous horse named “Clever Hans” turned out to be solving arithmetic problems with cues from the body language of nearby people. A different study finds that horses can tell two dots from three but might be using area as a clue.
Source: C. Uller and J. Lewis/Anim. Cogn. 2009 James Woolley/Flickr (CC BY-SA 2.0)

Dogs treat tricks

For a sense of the issues, consider the old and the new in dog science. Familiar as dogs are, they’re still mostly wet-nosed puzzles when it comes to their number sense.

When food is at stake, dogs can tell more from less. That is known from a string of lab studies published throughout more than a decade. And dogs may be able to spot cheating when people count out treats. Dog owners may not be amazed at such food smarts. The interesting question, though, is whether dogs solve the problem by paying attention to the actual number of goodies they see. Perhaps they instead note some other qualities.

An experiment in England in 2002, for instance, tested 11 pet dogs. These dogs first settled down in front of a barrier. The researchers moved the barrier so the animals could get a peek at a row of bowls. One bowl held a brown strip of Pedigree Chum Trek treat. The barrier went up again. The scientists lowered a second treat into a bowl behind the screen — or sometimes just pretended to. The barrier dropped again. The dogs overall stared a bit longer if only one treat was visible than if there were the expected 1 + 1 = 2. Five of the dogs got an extra test. And they also stared longer on average after a researcher sneaked an extra treat into a bowl and then lowered the barrier. It now displayed an unexpected 1 + 1 = 3.

Dogs could in theory recognize funny business by paying attention to the number of treats. That would be the treats’ numerosity. Researchers use this term that to describe some sense of quantity that can be recognized nonverbally (without words). But the design of a test also matters. Dogs might get the right answers by judging the total surface area of treats, not their number. Many other factors might also serve as clues. These include the density of a cluster of crowded objects. Or it might be a cluster’s total perimeter or darkness.

Researchers lump those hints under the term “continuous” qualities. That’s because they can change in any amount, big or small, not merely in separate units (such as one treat, two treats or three).

Continuous qualities present a real challenge for anyone coming up with a numerosity test. By definition, nonverbal tests don’t use symbols such as numbers. That means a researcher has to show something. And those somethings inevitably have qualities that grow or shrink as numerosity does.

Sedona’s sense of math

Krista Macpherson studies dog cognition at Canada’s University of Western Ontario in London. To see whether dogs use a continuous quality — total area — to choose more food, she tested her rough collie Sedona.

This dog already had taken part in an earlier experiment. In it, Macpherson tested whether dogs would try to get help if their owners were in danger. That’s what the collie did on the old TV show Lassie. But Sedona didn’t. For example, neither she nor any dog in the test ran for help when their owners were trapped under a heavy bookcase.

Sedona did, however, prove good at lab work — especially when rewarded with bits of cheese.

A low-tech setup tests this dog, Sedona, to see if she can pick the cardboard box showing a greater number of geometric cutouts on its face without being distracted by size or shape. K. MACPHERSON

To test number sense, Macpherson set up two magnetic boards. Each had different numbers of black triangles, squares and rectangles stuck to them. Sedona had to select the one that had the greater number. Macpherson varied the dimensions of the shapes. This meant total surface area wasn’t a good clue to the right answer.

The idea came from an experiment with monkeys. They had taken the test on a computer. But “I’m all cardboard and tape,” Macpherson explains. Sedona was perfectly happy to look at two magnet boards fastened to cardboard boxes on the ground. She then chose her answer by knocking over that box.

Sedona in the end triumphed at picking the box with more shapes. She could do this regardless of all the trickery about surface area. The project, though, took considerable effort from both woman and beast. Before it was over, both had worked through more than 700 trials.

For Sedona to succeed, she had to pick the larger number of shapes more than half of the time. The reason: Just picking randomly, the dog would probably choose correctly half of the time.

The tests started as simply as 0 shapes versus 1 shape. Eventually Sedona scored better than chance when dealing with bigger magnitudes, such as 6 versus 9. Eight versus 9 finally stumped the collie.

Macpherson and William A. Roberts reported their findings three years ago in Learning and Motivation.

Earlier this year, another lab highlighted the Sedona research in Behavioral Processes. Its researchers called the Sedona data the “only evidence of dogs’ ability to use numerical information.”

Dogs might have number sense. Outside of a lab, however, they may not use it, says Clive Wynne. He works at Arizona State University in Tempe. There he studies animal behavior. He’s also a co­author of that Behavioral Processes paper earlier this year. To see what dogs do in more natural situations, he designed a test along with Maria Elena Miletto Petrazzini of the University of Padua.

The pair offered pets at a doggie daycare a choice of two plates of cut-up treat strips. One plate might hold a few big pieces. The other had more pieces, all of them small. And the total of those smaller pieces added up to less of the yummy treat.

These dogs didn’t have Sedona’s training. Still, they went for the greater total amount of food. The number of pieces didn’t matter. Of course not. It’s food —and more is better.

This study shows that experiments need to check if animals use something like total amount instead of number. If not, the tests may not measure number sense at all.

Beyond dogs

Animals may choose differently in a number-related test depending on their pasts. At the University of Padua, Rosa Rugani studies how animals process information. She pioneered the study of number sense in newly hatched chicks. If Rugani motivates them, they will learn test methods quickly. Indeed, she notes, “One of the more fascinating challenges of my job is to come up with ‘games’ the chicks like to play.”

Young chicks can develop a strong social attachment to objects. Little plastic balls or lopsided crosses of colored bars become like pals in a flock. (This process is called imprinting. It normally helps a chick quickly learn to stay near its mom or siblings.)

Rugani let day-old chicks imprint on either two or three objects. She offered them either a few identical objects or a cluster of mismatched ones. The set of different pals were, for example, a small black plastic zigzag of rods dangling near a big red double-crossed t-shape. Chicks then had to choose to which flock of new and strange plastic objects they would toddle over.

The original imprinting objects — identical or mismatched — made a difference in that choice. Chicks used to identical pals typically moved near the larger cluster or toward the largest buddy. Something like total area might have been their clue. But chicks used to buddies with individual quirks paid attention to numerosity in the test.

Chicks that had imprinted on three plastic pals were more likely to hang out with three new ones instead of a pair. Those imprinted on a quirky plastic pair made the opposite choice. They chose the pair, not the threesome.

Some animals can deal with what people would call numerical order. Rats, for instance, have learned to choose a particular tunnel entrance, such as the fourth or tenth from the end. They could choose correctly even when researchers fiddled with distances between entrances. Chicks have passed similar tests.

Rhesus macaques react if researchers violate rules of addition and subtraction. This is similar to the dogs in the Chums experiment. Chicks can track additions and subtractions too. They can do this well enough to pick the card hiding the bigger result. They also can go one better. Rugani and colleagues have shown that chicks have some sense of ratios.

To train chicks, she let them discover treats behind cards showing a 2-to-1 mix of colored dots, such as 18 greens and 9 reds. There were no treats behind 1-to-1 or 1-to-4 mixes. Chicks then scored better than chance on picking unfamiliar 2-to-1 dot jumbles, such as 20 greens and 10 reds.

A sense of numerosity itself may not be limited to fancy vertebrate brains like ours. One recent test took advantage of overkill among golden orb-web spiders. When they have a crazy run of luck catching insects faster than they can eat them, the spiders wrap each catch in silk. They then fasten the kill with a single strand to dangle from the center of the web.

Rafael Rodríguez turned this hoarding tendency into a test. He studies the evolution of behavior at the University of Wisconsin–Milwaukee. In one test, Rodríguez tossed different sized bits of mealworms into the web. The spiders created a dangling trove of treasures. He then shooed the spiders off of their webs. That gave him the opportunity to snip the strands without the spiders watching. When they returned, Rodríguez timed how long they searched for the stolen meals.

Losing a greater volume of food inspired more strumming of the web and searching about. Rodríguez and his colleagues reported this last year in Animal Cognition.

At a glance

Nonhuman animals have what researchers refer to as an “approximate” number system. It allows for good-enough estimates of quantities with no true counting. One feature of this still-mysterious system is its declining accuracy in comparing bigger amounts that are very close in number. That’s the trend that made Sedona the collie’s struggles as important as her successes.

When Sedona had to pick the board with more shapes on it, she had more trouble as the ratio of choices moved toward nearly equal amounts. Her scores, for instance, were pretty good when comparing 1 to 9. They fell somewhat when comparing 1 to 5. And she never got good at comparing 8 to 9.

What’s interesting is that the same trend shows up in humans’ nonverbal approximate number system. This trend is called Weber’s law. And it also shows up in other animals.

Story continues below image.

Weber’s Law:

Quick, which of the two circles in each pair has more dots in it? Weber’s law predicts that the answer will come easier when object numbers in a pair are very different (8 versus 2) and/or involve a small number than when two large ones (8 versus 9) are compared. J. HIRSHFELD

When Agrillo tested guppies against people, their accuracy dropped during such difficult comparisons as 6 versus 8. But fish and people performed well for small quantities, such as 2 versus 3. People and fish could tell 3 dots from 4 about as reliably as 1 dot from 4. Agrillo and his colleagues reported their findings in 2012

Take a quick glance at the clusters here before reading more. You probably saw that the box on the left had three dots. But you’d have to count the mosquitoes on the right. That immediate grasp of small quantities is called subitizing, an ability that people and other animals may share. M. TELFER

Researchers have long recognized this instant human ease of dealing with very small quantities. They call it subitizing. That’s when you suddenly just see that there are three dots or ducks or daffodils without having to count them. Agrillo suspects the underlying mechanism will prove different from the approximate number systems. He admits, though, that his is a minority view.

The similarity between guppies and people in subitizing doesn’t prove anything about how that skill might have evolved, Argillo says. It could be a shared inheritance from some ancient common ancestor that lived several hundred million years ago. Or maybe it’s convergent evolution.

Into their heads

Studying behavior alone is not enough to trace the evolution of number savvy, says Andreas Nieder. He studies the evolution of animal brains at the University of Tübingen in Germany. Behavior in two animals may look alike. Yet the two brains may create that behavior in very different ways.

Nieder and his colleagues have started the huge task of looking at how brains develop a number sense. So far they have studied how monkey and bird brains handle quantity. The researchers compared nerve cells, or neurons, in macaques with those in the brains of carrion crows.

Research in monkeys over the last 15 years has identified what Nieder calls “number neurons.” They may not be just for numbers, but they do respond to numbers.

He proposes that one group of these brain cells gets especially excited when it recognizes one of something. It could be a crow or crowbar, but these brain cells will react strongly. Another group of neurons gets especially excited by two of something. Among these cells, neither one nor three of the somethings kicks off such a strong response.

Some of these brain cells respond to the sight of certain quantities. Others respond to certain numbers of tones. Some, he reports, respond to both.

These brain cells lie in important places. Monkeys have them in the multilayered neocortex. This is the “newest” part of an animal’s brain — the one that developed most recently in evolutionary history. It includes part of your brain in the very front (behind the eyes) and on the sides (above the ears). These areas allow animals to make complex decisions, to consider consequences and to process numbers.

Birds don’t have a multilayered neocortex. Yet Nieder and colleagues have, for the first time, detected individual neurons in a bird brain that respond much as a monkey’s number neurons do.

The bird versions lie in a relatively newfangled area of the avian brain (the nidopallium caudolaterale). It didn’t exist in the last common ancestor shared by birds and mammals. Those reptile-like beasts had lived some 300 million years ago and they didn’t have a primate’s precious neocortex either.

Story continues below image.

Bird brains lack a fancy six-layered outer cortex. But carrion crows (right) have a brain area called the nidopallium caudolaterale that is rich in nerve cells that respond to quantity. In the macaque (left), number neurons are in a different area, mainly a region known as the prefrontal cortex. A. NIEDER/NAT. REV. NEUROSCI. 2016

So birds and primates probably did not inherit their considerable skill with quantities, Nieder says. Their number neurons could have become specialized independently of each other. As such, this is probably convergent evolution, he argued in the June 2016 Nature Reviews Neuroscience.

Finding some brain structures to compare across deep time is a promising step in figuring out the evolution of number sense in animals. But it’s just a beginning. There are many questions about how the neurons work. There also are questions about what’s going on in all of those other brains that evaluate quantity. For now, looking across the tree of life at the crazy abundance of number smarts, the clearest thing to say may just be Wow!

Power Words

array A broad and organized group of objects. Sometimes they are instruments placed in a systematic fashion to collect information in a coordinated way. Other times, an array can refer to things that are laid out or displayed in a way that can make a broad range of related things, such as colors, visible at once.

average (in science) A term for the arithmetic mean, which is the sum of a group of numbers that is then divided by the size of the group.

avian Of or relating to birds.

bat A type of winged mammal comprising more than 1,100 separate species &mdash or one in every four known species of mammal.

behavior The way a person or other organism acts towards others, or conducts itself.

birds Warm-blooded animals with wings that first showed up during the time of the dinosaurs. Birds are jacketed in feathers and produce young from the eggs they deposit in some sort of nest. Most birds fly, but throughout history there have been the occasional species that don&rsquot.

breed (noun) Animals within the same species that are so genetically similar that they produce reliable and characteristic traits. German shepherds and dachshunds, for instance, are examples of dog breeds. (verb) To produce offspring through reproduction.

carrion The dead and rotting remains of an animal.

cell The smallest structural and functional unit of an organism. Typically too small to see with the naked eye, it consists of watery fluid surrounded by a membrane or wall. Animals are made of anywhere from thousands to trillions of cells, depending on their size. Some organisms, such as yeasts, molds, bacteria and some algae, are composed of only one cell.

cognition The mental processes of thought, remembering, learning information and interpreting those data that the senses send to the brain.

colleague Someone who works with another a co-worker or team member.

control A part of an experiment where there is no change from normal conditions. The control is essential to scientific experiments. It shows that any new effect is likely due only to the part of the test that a researcher has altered. For example, if scientists were testing different types of fertilizer in a garden, they would want one section of it to remain unfertilized, as the control. Its area would show how plants in this garden grow under normal conditions. And that give scientists something against which they can compare their experimental data.

convergent evolution The process by which animals from totally unrelated lineages evolve similar features as a result of having to adapt to similar environments or ecological niches. One example is how some species of ancient marine reptiles called ichthyosaurs and modern-day dolphins evolved to have remarkably similar shapes.

cortex The outermost layer of neural tissue of the brain.

crow The characteristic loud cry of a rooster. (in biology) A type of large black bird with a complex social structure that perches in trees and is known for its boisterous call.

density The measure how condensed an object is, found by dividing the mass by the volume.

diversity (in biology) A range of different life forms.

evolution (v. to evolve) A process by which species undergo changes over time, usually through genetic variation and natural selection. These changes usually result in a new type of organism better suited for its environment than the earlier type. The newer type is not necessarily more &ldquoadvanced,&rdquo just better adapted to the conditions in which it developed.

evolutionary An adjective that refers to changes that occur within a species over time as it adapts to its environment. Such evolutionary changes usually reflect genetic variation and natural selection, which leave a new type of organism better suited for its environment than its ancestors. The newer type is not necessarily more &ldquoadvanced,&rdquo just better adapted to the conditions in which it developed.

hypothesis A proposed explanation for a phenomenon. In science, a hypothesis is an idea that must be rigorously tested before it is accepted or rejected.

insect A type of arthropod that as an adult will have six segmented legs and three body parts: a head, thorax and abdomen. There are hundreds of thousands of insects, which include bees, beetles, flies and moths.

macaque A monkey with cheek pouches and a short tail that lives mainly in the forest.

magnet A material that usually contains iron and whose atoms are arranged so they attract certain metals.

mammal A warm-blooded animal distinguished by the possession of hair or fur, the secretion of milk by females for feeding the young, and (typically) the bearing of live young.

mealworm A wormlike larval form of darkling beetles. These insects are found throughout the world. The ever-hungry wormlike stage of this insect helps break down &mdash decompose, or recycle &mdash nutrients back into an ecosystem. These larvae also are commonly used as a food for pets and some lab animals, including chickens and fish.

mechanism The steps or process by which something happens or &ldquoworks.&rdquo It may be the spring that pops something from one hole into another. It could be the squeezing of the heart muscle that pumps blood throughout the body. It could be the friction (with the road and air) that slows down the speed of a coasting car. Researchers often look for the mechanism behind actions and reactions to understand how something functions.

nerve A long, delicate fiber that communicates signals across the body of an animal. An animal&rsquos backbone contains many nerves, some of which control the movement of its legs or fins, and some of which convey sensations such as hot, cold, pain.

neuron The impulse-conducting cells that make up the brain, spinal column and nervous system.

neuroscience The field of science that deals with the structure or function of the brain and other parts of the nervous system. Researchers in this field are known as neuroscientists.

nonverbal Without words.

numerical Having to do with numbers.

numerosity The term scientists give to a quantity recognized nonverbally.

perimeter The outer border or edge of some defined area. For instance, the perimeter of some people&rsquos property is set off by a fence.

prefrontal cortex A region containing some of the brain&rsquos gray matter. Located behind the forehead, it plays a role in making decisions and other complex mental activities, in emotions and in behaviors.

primate The order of mammals that includes humans, apes, monkeys and related animals (such as tarsiers, the Daubentonia and other lemurs).

psychologist A scientist or mental-health professional who studies the human mind, especially in relation to actions and behavior.

ratio The relationship between two numbers or amounts. When written out, the numbers usually are separated by a colon, such as a 50:50. That would mean that for every 50 units of one thing (on the left) there would also be 50 units of another thing (represented by the number on the right).

reptile Cold-blooded vertebrate animals, whose skin is covered with scales or horny plates. Snakes, turtles, lizards and alligators are all reptiles.

reward (In animal behavior) A stimulus, such as a tasty food pellet, that is offered to an animal or person to get them to change their behavior or learn a task.

rhesus monkey (also called rhesus macaque) A small brown macaque with red skin on the its face and rump, native to southern Asia. It is often kept in captivity and is widely used in medical research.

savvy The quality of possessing useful and clever knowledge.

silk A fine, strong, soft fiber spun by a range of animals, such as silkworms and many other caterpillars, weaver ants, caddis flies and &mdash the real artists &mdash spiders.

social (adj.) Relating to gatherings of people a term for animals (or people) that prefer to exist in groups. (noun) A gathering of people, for instance those who belong to a club or other organization, for the purpose of enjoying each other&rsquos company.

species A group of similar organisms capable of producing offspring that can survive and reproduce.

spider A type of arthropod with four pairs of legs that usually spin threads of silk that they can use to create webs or other structures.

subitizing An instant ease in recognizing quantities without having to count them, such as when someone sees a trio of ducks and knows that there are three of them without having to count them.

surface area The area of some material&rsquos surface. In general, smaller materials and ones with rougher or more convoluted surfaces have a greater exterior surface area &mdash per unit mass &mdash than larger items or ones with smoother exteriors. That becomes important when chemical, biological or physical processes occur on a surface.

theory (in science) A description of some aspect of the natural world based on extensive observations, tests and reason. A theory can also be a way of organizing a broad body of knowledge that applies in a broad range of circumstances to explain what will happen. Unlike the common definition of theory, a theory in science is not just a hunch. Ideas or conclusions that are based on a theory &mdash and not yet on firm data or observations &mdash are referred to as theoretical . Scientists who use mathematics and/or existing data to project what might happen in new situations are known as theorists.

tissue Any of the distinct types of material, comprised of cells, which make up animals, plants or fungi. Cells within a tissue work as a unit to perform a particular function in living organisms. Different organs of the human body, for instance, often are made from many different types of tissues. And brain tissue will be very different from bone or heart tissue.

tree of life A diagram that uses a branched, treelike structure to show how organisms relate to one another. Outer, twiglike, branches represent species alive today. Ancestors of today&rsquos species will lie on thicker limbs, ones closer to the trunk.

undergraduate A term for a college student &mdash one who has not yet graduated.

vertebrate The group of animals with a brain, two eyes, and a stiff nerve cord or backbone running down the back. This group includes amphibians, reptiles, birds, mammals and most fish.

Citations

Journal: R. Rugani et al. Ratio abstraction over discrete magnitudes by newly hatched domestic chicks (Gallus gallus). Scientific Reports. Vol.6, published online July 28, 2016, p. 30114. doi: 10.1038/srep30114.

Journal: A. Nieder. The neuronal code for number. Nature Reviews Neuroscience. Vol. 17, June 2016, p. 366. doi: 10.1038/nrn.2016.40.

Journal: M.E. Miletto Petrazzini et al. Do humans (Homo sapiens) and fish (Pterophyllum scalare) make similar numerosity judgments? Journal of Comparative Psychology. Vol.130, November 2015, p. 380. doi: 10.1037/com0000045.

Journal: H. Ditz and A. Nieder. Neurons selective to the number of visual items in the corvid songbird endbrain. Proceedings of the National Academy of Sciences. Vol. 112, June 23, 2015, p. 7827. doi: 10.1073/pnas.1504245112.

Journal: K. Macpherson and W.A. Roberts. Can dogs count? Learning and Motivation. Vol. 44, November 2013, p. 241. doi: 10.1016/j.lmot.2013.04.002.

Journal: L. Cantrell and L.B. Smith. Open questions and a proposal: A critical review of the evidence on infant numerical abilities. Cognition. Vol. 128, September 2013, p. 331. doi: 10.1016/j.cognition.2013.04.008.

Journal: C. Agrillo et al. Evidence for two numerical systems that are similar in humans and guppies. PLOS ONE. Vol. 7, February 2012, p. e31923. doi: 10,1371/journal.pone.0031923.

Journal: K. Macpherson and W.A. Roberts. Do dogs (Canis familiaris) seek help in an emergency? Journal of Comparative Psychology. Vol. 120, May 2006, p. 113. doi: 10.1037/0735-7036.120.2.113.

Journal: R. Rugani et al. Arithmetic in newborn chicks. Proceedings of the Royal Society B. Vol. 276, July 7, 2009, p. 2451. doi: 10.1098/rspb.2009.0044.

Journal: R. West and R.J. Young. Do domestic dogs show any evidence of being able to count? Animal Cognition. Vol.5, September 2002, p. 183. doi: 10.1007/s10071-002-0140-0.

About Susan Milius

Susan Milius is the life sciences writer, covering organismal biology and evolution, and has a special passion for plants, fungi and invertebrates. She studied biology and English literature.

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