Figure 1:All ladders do something interesting: They divide vertical space in discrete, countable steps with nothing (but air) in between. The result is that we can count height in steps we take up or down. Ladders thus apply an (arbitrary) scale of sorts to height and thus provides countable units that we can add, divide, and so on. What does that have to do with the science of perception? There is an intriguing analog that has revolutionized how we think of the measurability of conscious experience.[1]
Figure 1:All ladders do something interesting: They divide vertical space in discrete, countable steps with nothing (but air) in between. The result is that we can count height in steps we take up or down. Ladders thus apply an (arbitrary) scale of sorts to height and thus provides countable units that we can add, divide, and so on. What does that have to do with the science of perception? There is an intriguing analog that has revolutionized how we think of the measurability of conscious experience.[1]
Motivation¶
Before we discuss each of our senses in detail, we first need to take a brief historical detour. The reason for that is an interesting one.
Much of what we will discuss in the context of the science of perception will be anything but. For example, we will discuss the physics of light, sound, and mechanical force as well as the chemistry of odorants and gustation. These are all stimuli of our environment that we can sense. However, by themselves they do not lead to perception: According to physics, light inside a room inside a vacated home exists no matter whether there is someone perceiving it or not.
We then will discuss how our bodies sense these stimuli, such as how photoreceptors react to light. But that, too, seems to have little to do with perception. After all, we can have visual experiences at night in a dark room with eyes closed when we dream. And on the flip side, we seem to not perceive anything even with our eyes open when we are unconscious because we fainted or undergo general anesthesia.
You might suspect that perception is more closely linked with what your brain does after it receives information from your sense receptors, and that is correct. But, as well see, even this line of inquiry does not get very far - all we will be able to find are brain mechanisms that correlate with perception, such as neurons or areas that increase or decrease in activity whenever we have a certain perceptual experience.
For this reason we will also review what is known about the psychology of perception, with the ultimate goal to find a link between how perception presents itself to us and the brain mechanisms that support it. But this is where a problem arises.
How can be scientific about perception? How can we measure it? Put numbers on it?
At first sight it seems that perception is “too subjective” for “objective” measurement. And in fact, this was the prevailing view of scholars for long periods of history. Some of that skepticism persists. You can still buy stickers online that proclaim “You cannot measure love.”, suggesting that feelings (which we defined to be perceptual experiences about our own mental state) are fundamentally unmeasurable. That seems inuitive, but as we will see, it is incorrect.
Figure 3:Measurement is essential for exact science. But (how) can we precisely measure perception? [2]
Can you measure love?¶
Imagine your best friend tells you that they have recently fallen in love. Asking them: “That is wonderful. How much?” will likely just evoke a confused smile.
But is it really an unanswerable question? After all, it may make sense that they have fallen in love before and that the experience is not the same this time.
It is not unheard of that people who find “the love of their life” experience that their love for this person is greater than what they have felt before.
In the same vein, some parents experience that their love for their children leads them to a previously unexperienced form of love: Many parents would gladly lay down their lives for ther children and have not felt that before. This is not to take away from the love they feel for other people, of course. It just seems that they experience even more love for their children.
Figure 4:Is it really true that “You cannot you measure love?” [3]
And what is measurement other than assessing “more”, “less”, or “the same”? Numbers seem to make this process just a bit more precise.
Still, you might feel hesitant to judge what someone perceives by them assigning numbers to it. Not only is perception “subjective”, but assigning a value seems “subjective” as well.
Perhaps surprisingly, we have learned that neither seems to be a fundamental problem. In fact, we make life-or-death decisions based on such self-assigned numbers to perceptual experiences. But before we get to that, we first need to follow the historical arc that led to such a drastic outcome.
History¶
The finding that we can make precise measurements of perception only goes back to 1850. On October 22 that year, Gustav Theodor Fechner made an entry in his diary that he had a conceptual breakthrough. We are still making use of that insight today, including people that have made millions of dollars based on it.
So, what Fechner did find?
His insight is best understood by a thought experiment:
Imagine you are blindfolded. You are stretching out one of your arms. Someone places a small, thin sheet paper on it. Can you feel it?
Figure 5:Imagine being blindfolded with the aim to feel changing weights in your hands. [4]
Now imagine that the other person silently places a large feather on your hand with the paper on it. Your task is to speak up when you feel that extra weight. If you think that you could probably detect that change in weight, you are probably right.
But now imagine that that person neatly placed 100 feathers on top of the paper. So, your hand now feels quite a bit heavier. And the task is now to detect a single extra feather. Would that be possible? What if we start with 500 feathers? Or 5000? Would you still be able to feel when a single extra feather is added? If your intuition is that this would be harder, if not impossible, you are correct.
This seems trivial. But Fechner realized that something very interesting happened here.
Figure 6:How many feathers can a blindfolded person tell apart if they are slowly added to a plate they hold in their hand?[5]
Let us imagine that when we added the first feather you sensed a difference in weight. And we already established that once there are many (hundreds or thousands of feathers), you cannot sense the same difference in weight. What this means is that if we imagine that we just add one feather at a time and your task is to detect and say when that happened, we will go from you sensing every physical change (each added feather) to - at some point - *having the same (constant) perception despite the physical stimulus increasing.
Again, this may seem trivial, but we are not quite done yet. Now, imagine that we added so many feathers to your hand that you do not feel anymore when a single feather is silently added. But if we keep adding feathers, at some point you will! After all, only because your hand feels heavier now and you cannot feel a single feather being added anymore does not mean that you lost all sense of weight. Maybe we need to add 10 more feathers or 100, but at some point you will say “Now it feels heavier again”.
Taken all this into account, Fechner realized that often we fail to detect small changes of physical stimuli, such as the added weight of a feather when our hand already holds up something slightly heavier. And that this state of feeling the same despite the stimulus changing can persist across several steps of physical changes, such as adding yet another feather. We call this state of affairs being at “subjective equality” - no matter the fact that the physical stimulus is getting heavier, you feel all these weights as subjectively equal.
Now, even more interesting is what happens next: The moment we add so many new feathers that you eventually feel an increase in weight. This is a threshold. That is, we finally crossed a threshold of adding weight that broke you out of subjective equality.
Thresholds¶
Why is this a big deal? Remember that we started out by pondering that we cannot put numbers of perception (such as love). But a threshold allows us to do just that! You went from 0 (no change/feels the same) to 1 (feels like “more”). And this is not just an arbitrary “step”. The “more” that you feel once we pass the threshold is the minimal amount of “more weight” that you can feel under these circumstances. After all, if there would have been a smaller increment, you would have felt that. But instead, you felt no change.
Do you see why Fechner got excited? He just solved the problem. We can put numbers on our perception, they are not arbitrary but measure minimal perceptual increments, and we can do all that using experiments. All we have to do is to precisely measure when these thresholds occur - the respective change in physical stimulus is called the just-noticeable difference, or JND.
But there is more. We can also find out when you go from perceiving nothing to perceiving something using the same technique. This is just another threshold. For example, we can play very faint sounds or use very dim lights, make them stronger and find out when you hear or see the stimulus. These thresholds (the minimal stimulus intensities that you can perceive) are called absolute thresholds since they are believed to be more or less unchanging for the same individual (different people, such as when testing the faintest sound young or old people can hear, have very different absolute thresholds, of course). Stimuli that are just above the absolute threshold are called just noticeable stimuli. Different people tested at different times will have different absolute thresholds.
In contrast, the thresholds that occur when we start out with you already perceiving a stimulus (such as the weight of a single feather), and ramp up the stimulus intensity (e.g., buy adding more feather) are called relative thresholds. That implies that may not be a constant, but instead what we experience as a relative threshold depends on what we just experienced. However, this does not imply that relative thresholds are random. Instead, they follow a rule (which we will discuss in the next section). Showing that this context-dependence is not arbitrary was Fechner’s second major breakthrough. Stimuli that pass a relative threshold (and thus evoke a change in perception) are called just noticeable differences, or JNDs.
The measure of a JND is crucial for mathematizing perception. Since our perception is unchanged if we change a stimulus just barely so that it remains below a relative threshold means that our perception “jumps” in discrete steps, where each step up is a JND. In other words, perception seems to have units in which it increases in magnitude. We can count these steps and assign numbers to them. The result is a staircase of sorts, where our perception is “flat” (unchanged) for small stimulus changes and then “steps up” at each relative threshold and thereby increases by one JND.
When we slightly change a stimulus and we do not experience a difference in our perception (despite the physically changed stimulus), we call these “flat” parts of the staircase points of subjective equilibrium, or PSE. This is just a fanciful label for describing that our perception is unchanged, even though we changed stimulation.
This all might sound a bit convoluted (and certainly is quite a bit of jargon), which might distract from the fact that what we are describing is quite simple and straightforward, perhaps even a bit trivial. The easiest way to demonstrate what we just described is via illustration:
Figure 7:The leftmost images show 10 and 20 dots, respectively. We can immediately tell that the bottom image shows more dots (a higher quantity) than the one above. Psychophysically speaking, the two images must be two stimuli separated by one or more just-noticeable-differences (JNDs) for us to be able to tell that they are different (in amount of dots). However, the rightmost two images look like they are of the amount - even though the bottom image again features 10 dots more than the image above. Psychophysically speaking, these two images fall inside a point of subjective equality (PSE). That is, we experience them as being of the same amount, despite the fact that the actual physical amount differs (interestingly enough by the same amount, 10 dots, that we were able to immediately detect as added).[5]
![The leftmost images show 10 and 20 dots, respectively. We can immediately tell that the bottom image shows more dots (a higher quantity) than the one above. Psychophysically speaking, the two images must be two stimuli separated by one or more just-noticeable-differences (JNDs) for us to be able to tell that they are different (in amount of dots). However, the rightmost two images look like they are of the amount - even though the bottom image again features 10 dots more than the image above. Psychophysically speaking, these two images fall inside a point of subjective equality (PSE). That is, we experience them as being of the same amount, despite the fact that the actual physical amount differs (interestingly enough by the same amount, 10 dots, that we were able to immediately detect as added).[^6]](/sensation/build/PSE-f6fc218e2bad1141a3f5d5281780fa65.png)
Figure 7:The leftmost images show 10 and 20 dots, respectively. We can immediately tell that the bottom image shows more dots (a higher quantity) than the one above. Psychophysically speaking, the two images must be two stimuli separated by one or more just-noticeable-differences (JNDs) for us to be able to tell that they are different (in amount of dots). However, the rightmost two images look like they are of the amount - even though the bottom image again features 10 dots more than the image above. Psychophysically speaking, these two images fall inside a point of subjective equality (PSE). That is, we experience them as being of the same amount, despite the fact that the actual physical amount differs (interestingly enough by the same amount, 10 dots, that we were able to immediately detect as added).[^6]
[6]: public domain image source
Let’s go back to our thought experiment. We established that if you hold your hand out, and we put the light weight of a piece of paper on top of it, you will likely feel the weight of a single feather that we lay on top of the paper (if you cannot imagine that, just imagine it being 10 feathers at once). Now imagine that we put several very big hardcover books on your hands and add the feather (or 10 feathers) again. Would you be able to feel that? No. Clearly. So, the threshold of, say a single (or 10) feathers now does not work anymore. We need a lot more feathers on top of the books before you feel the extra weight.
Fechner’s Law¶
Fechner went to work and tested exactly that. Rather than a thought experiment, he tested what the exact weights were that blindfolded people could detect. And he realized something astonishing: The relative thresholds increased proportionally to the weight that the person already had in hand.
Let us take a moment and ponder that. Fechner did not only show that we can measure (changes in) perception numerically, but that if we do so, the result follows a mathematical law!
And that law takes the mathematical shape of a logarithm:
where S is the perceived magnitude I is the physical stimulus I0 is the minimally detectable stimulus k is a constant that changes depending on the type of sense or stimulus
There is a mathematically precise law that allows us to predict how perception changes as we increase or decrease the strength (magnitude) of a physical stimulus. And that relationship, or mapping, between physical stimuli and perceptual experience is logarithmic (in most cases - we will discuss exceptions later).
Fechner realized that this meant that perception seemed to follow “laws of nature”, just like the classical Newtonian physics that he was familiar with. That is, we can describe perceptual measurement with equations, just like we can describe motion with equations (such as F=ma). Fechner thus called his approach Psychphysics since it really seemed to be a “physics of the psyche” in that it is an approach of precise measurement resulting in lawful relations (and hence predictions).
Methods¶
You might feel a bit concerned at this point that, while we celebrated a mathematically rigorous law (Fechner’s Law), we seemingly started without a rigorous experimental approach. After all, we just imagined a scenario where someone is blindfolded, we change the physical stimulus and await a response. But what if that person is lying (perhaps just because they find that funny)?
Psychophysics found clever ways around that potential problem. So, let’s talk about that next.
There are three “classical methods” that we will discuss first. After that, we will discuss some clever extensions that have become feasible thanks to additional mathematics and computer technology that further minimize unreliable data from untruthful - and even from just slightly biased - observers.
Method of Constant Stimuli¶
This technique is the most straightfoward. We prepare a set of stimuli of varying intensity (such as different weights), and randomly present them to a voluntary participant. Then, we determine which stimuli were above or below the absolute threshold of detection in order to determine the minimal detectable stimulus, or just detectable stimulus. In order to obtain reliable data, we can repeatedly present the stimuli to determine an average.
Method of Adjustment¶
This technique is distinguished by the participant changing the stimulus themselves.