On Psychophysics and the Laws of Sukkah (Column 99)
Colors and sounds are not 'out there' but our way of translating the world
The essay opens with a Kantian-scientific claim: in the world itself there are electromagnetic waves, pressure waves, and the like, while colors, sights, and sounds are the way our consciousness translates them. So one can in principle imagine creatures that 'see' sounds or 'hear' sights, and even phenomena that our senses do not register at all. This is not a metaphor but a description of the structure of human perception.
Why this picture does not abolish objective truth, and where the 'philosophers’ chestnut' still remains
R. Avraham distinguishes between the first half of the description — what exists in the physical world — and the second half — how that appears in my consciousness. The first half can be a single objective truth even if each creature 'translates' it differently; in that sense this is not relativism. And yet a limited skeptical difficulty remains: we have no way to know whether, when two people say 'red,' they experience the same subjective quality, and perhaps one of them experiences something of an entirely different kind. This dimension is accessible only through language, and therefore cannot be objectively verified.
Psychophysics tests the relation between physical intensity and experience, but may be asking a question with no metric
From here the essay turns to psychophysics: researchers compare the intensity of a physical stimulus with the subject’s reports about the intensity of the experience, and propose linear, logarithmic, or power-law models. But R. Avraham makes a sharper claim than the disagreement among those models: when a person is asked whether the new light is 'twice' the previous one, it is not clear that the problem is only that his answer is hard to measure; the question itself may be undefined. To say that there is more light or less light is meaningful, but assigning numerical ratios between subjective intensities may resemble a meaningless question, like comparing the amount of water in the ocean to human kindness.
Rashi’s reading in Sukkah: invalidity is determined by the sun and shade on the ground, and that creates a double difficulty
The essay brings Rashi on the mishnah 'if its sunlight exceeds its shade,' who explains the invalidity through nullification by majority. This implies that on his view the focus is the sunlight and shade on the floor of the sukkah, not only the ratio between sekhakh and open space above; otherwise there would have been no need to invoke nullification. The commentators object to applying nullification by majority when the components are distinct, but R. Avraham points to an earlier difficulty: in reality we do not see simple 'patches of sun' and 'patches of shade' on the ground, but a uniform gray produced also by diffraction, refraction, and interference of light.
If we go by the shade of gray on the ground, halakha turns into a psychophysical experiment
Here the halakhic-philosophical problem appears: in order to determine whether the ground is in a state of 'more sun than shade,' one would seemingly have to compare three subjective states — full light, full darkness, and the gray in between — and decide whether that gray is above or below the halfway point. This is exactly a psychophysical comparison of light intensities. Without measuring instruments, Hazal and the Rishonim had no way to do this, and even conceptually it is not clear that it makes sense to say that the present sensation is 'half' of full light. Therefore the law cannot be grounded in the experience of illumination as it is actually perceived.
The solution: a halakhic model of geometric optics instead of the phenomenal description
The conclusion is that halakha does not need to measure the subjective sensation of light; it adopts an ideal model instead: straight light rays, area ratios between sekhakh and open space, and a hypothetical reckoning of sunlight and shade on the ground. Within that framework one can say that a given case 'counts' as mostly sun even if, in practice, all that appears is a gray tone that we do not know how to evaluate. This also fits the fact that throughout the laws of sukkah we already ignore real-world data such as the shade cast by the walls, nearby objects, and the actual position of the sun. At the end, R. Avraham leaves open a broader question: to what extent halakha deals with reality itself, and to what extent with the models through which we perceive and calculate it.
With God’s help
In this column I want to address a philosophical-scientific-halakhic issue. We apprehend the world around us by means of our cognitive faculties, that is, the senses. Kant already pointed out that what we refer to as the external world is not really the world itself (the noumenon), but the world as it is reflected in our cognition through our senses (the phenomenon). Thus, for example, there is no yellow or green color in the world. What there is is a physical phenomenon that emits or reflects an electromagnetic wave of a certain wavelength. When that wave strikes our retina, an image of yellow or green light is formed within our consciousness. In the world itself there is no light, nor color; there are only various electromagnetic waves. Our cognition translates them and creates within us colored images that exist only inside us and not in the external world. When I see a blue table before me, the blue color—and indeed the very appearance of the table—exists only in my consciousness. In the world itself there is no such appearance, nor are there colors. The image I see is a translation of physics into the terms of my cognition.
There is a well-known question about a tree that falls in a forest: does it make a sound even if no one is there? Contrary to what many think, the answer is of course no. It does not produce any sound at all; it merely moves air and creates a pressure wave (an acoustic wave). When such a wave strikes the eardrum of a human ear (or that of another animal), what we call sound is produced within our consciousness. Again, the wavelength and intensity of the acoustic wave create different sounds in our cognition, but in the world itself there are no sounds of any kind. There are only acoustic waves.
A Look at Other Creatures
To understand this better, imagine a creature whose eardrum and ear are connected to the visual center of its brain. That creature would see sounds. By the same token, there could be creatures that hear sights, if the retina in their eyes were connected to the auditory center in their brain. What would arise in them would be a state similar to what the Torah describes regarding the revelation at Mount Sinai, when the Jewish people saw the sounds (“saw the sounds”). (This is essentially what happens on an oscilloscope when an acoustic oscillator is connected to it.) In fact, there could also be creatures endowed with a completely different kind of brain from ours, that is, with modes of perception entirely unfamiliar to us. They might translate sights or sounds into kinds of perception wholly unknown to us. It is possible, and even likely, that there are phenomena in the world that our senses are simply incapable of perceiving, and therefore they are not translated into our consciousness and we know nothing of their existence (such as light at invisible wavelengths, or sound at ultrasonic frequencies, and the like).
Does This Amount to a Skeptical Picture?
Many people mistakenly think that this description leads to skepticism or conceptions of relative truth (relativism), but that is not so. This description in itself is a fact. Whoever disagrees with it simply does not understand it. All it does is clarify what it is we are dealing with. It does not mean that each of us sees the world differently, or that what we see does not reflect reality. What we see can certainly reflect reality quite well; it is simply that the appearance in our consciousness is a translation of what happens in the world, not an appearance of the world itself. In fact, there is no such thing as “an appearance of the world itself,” since an appearance always exists in the consciousness of the perceiver.
Therefore, no skeptical conclusions should be drawn from this. It is entirely possible that what we see is the very truth, except that this truth is translated into terms drawn from our consciousness. When we say that there is yellow light in the room, that may be the one pure truth, and even if someone else hears the electromagnetic wave in the room (that is, perceives it through his auditory center), he would have to translate our statement into a form that would be true for him as well: there is in the room an electromagnetic wave of such-and-such a wavelength. In conversation among human beings, this is translated into the sentence “there is yellow light in the room,” because we assume that we all translate it in the same way (see further below on this).
In fact, the full description is: “There is in the room an electromagnetic wave of such-and-such wavelength and intensity, and this produces yellow light in my consciousness.” Another creature would necessarily agree with the first part, but not necessarily with the second. The first part is a true description of the world, accepted by everyone regardless of his means of perception and cognition, whereas the second part is a description (entirely true as well) of what occurs within my own consciousness. If you like, you may call this a description in my subjective language. Even when I describe what is happening in the world in English and someone else describes it in Hebrew, it would not be correct to say that there is a disagreement between us. It is a description of the same thing in different languages.
And Yet Skepticism: the Philosophers’ Chestnut
However, the second part raises a difficult question, probably one with no solution at all, which some have called “the philosophers’ chestnut.” We saw that if Reuven and Shimon say they see a red cloth before them, this means that in the world itself there is a specific electromagnetic wave, and that is a fact on which both agree. But what about the red color in their inner consciousness? Do they both really have the same image in consciousness? Is what Reuven calls the color red what Shimon calls the color red? It may be that Shimon in fact sees what Reuven calls green light, but his mechanism of translation is different. An electromagnetic wave that is translated for Reuven as red (like the wave emitted by the piece of cloth mentioned above) is translated for Shimon as green. But both have been accustomed since birth to calling that “red.” Therefore both speak of seeing red cloth, but in fact what stands before their consciousness is a completely different color, or rather a completely different image.
Here there is already a skeptical dimension, for at least regarding the second part of the sentence—the part that describes what happens in our consciousness and not in the world itself—it is possible that we see completely different images, even though we use the same words to describe them. In fact, what appears to Reuven as red cloth may appear to Shimon as audio—for example, a melody from a violin concerto—except that this is what he has learned to express in the sentence “I see red light.” Thus they converse with one another, understand one another, agree completely, and in the world itself it is indeed the same phenomenon, but in their consciousness utterly different images appear.
As far as I know, there is no way to decide this question. Our subjective dimension is not accessible to objective measurements, and it is exposed to others only by way of verbal description. But the meaning of verbal description always depends on habit and language, and we have no way to verify that when we speak about the same thing we are indeed also observing the same cognitive image. It is impossible to synchronize two mental images, and indeed two systems of mental concepts. But as noted, all our descriptions and claims concern the mental and not the world itself.
I now want to point to a less familiar aspect of this picture, one that may actually have implications for discourse between human beings: perception and psychophysics.[1]
What Is Psychophysics?
Psychophysics deals with the relation between the physical and the psychical. What we described above is the philosophical foundation of this field, but surprisingly it turns out that scientific research is conducted in it. You may ask: how can one conduct scientific research on our subjective perceptions if they are not accessible to scientific measuring instruments? That, precisely, is the fundamental problem of this field. Usually the researchers obtain the data from the subjects’ reports and examine the relation between what they describe and reality.
For example, one seats a person in a room and illuminates the room around him with light, that is, one introduces an electromagnetic field of some intensity ø. One then doubles the intensity of the light, that is, the intensity of the electromagnetic field (or its square) is twice the previous one, 2ø. The same person is asked by what factor the intensity of the new light (P) is greater than that of the previous one. We have no way of knowing the intensity of the light that this person sees in his consciousness, since it is not accessible to measuring instruments. Therefore, our measure of the light intensity in his consciousness is solely his report. The purpose of such an experiment is to examine the dependence between ø and P. Alternatively, one begins gradually increasing the intensity and asks him to say when we have reached double intensity, and perhaps also to describe at each stage by what factor the intensity of the light has increased. From these reports a graph is constructed and compared with the intensities of the field (ø) as measured by scientific instruments.
The answers obtained in such experiments are of course not uniform. If this is done with many subjects, and their answers are averaged, one can plot a graph of subjective light intensity (P, what the subjects report) against physical light intensity (ø, what is measured by the instruments). The simple assumption is that the relation is linear, that is, that there is direct proportionality between these two variables. According to this assumption, the graph is a straight line, for example P=alpha*ø. Linear dependence means that doubling the field intensity creates a doubled light intensity in consciousness, and so too for any degree of increase whatever. But it turns out that the situation is not so simple. Different experiments yield different curves, and therefore there are different schools among the researchers regarding this dependence. At one time it was believed that the dependence was logarithmic: P=alpha*logø. In such a dependence, doubling the field intensity (ø) becomes an addition in the light intensity (P). This is a very weak dependence (a large change in field intensity produces a rather small change in light intensity). Others agree that these are straight lines, but there is a dispute regarding the slopes. There are schools that advocate non-straight curves, and today it is commonly thought that the dependence is some kind of power law, for example: P=alpha*ø^ε. There are, of course, disputes about the values of alpha and ε.[2]
In light of what I described above, it is clear that there is no right and wrong here, nor a good and reliable perception as opposed to defective perceptions. Each person describes what his system of translation yields. There is no truth and falsehood here. The question is how our systems of perception and translation are constructed. This is not a matter of diagnosing normal and defective systems.
But here I want to make a stronger claim. Even if we take a single individual and conduct the experiment on him, not only is there no right and wrong here; in fact, that person is answering a question that it is not clear he can really answer, and perhaps it is not even clear whether it has any meaning at all. What is the meaning of the statement “the light is now twice as intense as the previous light”? What is the metric for the intensity that I see in consciousness? Can one really speak of intensities and ratios between them? The question here is twofold: 1. A technical question: how can this be measured? If a person wants to give such an answer and determine whether the light that appears in his consciousness is double the previous one, or perhaps three times or ten times, on what basis can he determine this? How does he know that it is really double? 2. It may be that the question is even deeper and more fundamental: is there any correct answer at all? Perhaps this is not merely a technical problem of measurement, but actually a question with no answer. Perhaps there are no ratios between subjective intensities of light because they cannot be quantified. I am really wondering here whether such a question is not akin to the question: which is greater, the amount of water in the ocean or the good-heartedness of human beings? This is not a question for which we merely have a technical difficulty in providing an answer. The question itself is meaningless. In fact, it has no answer at all.[3]
I will now present a halakhic implication of the picture described here.
More Sun than Shade — Rashi’s Approach
The first Mishnah in tractate Sukkah concludes with the following rule:
If its sunlight exceeds its shade, it is invalid.
On this Rashi writes there:
If its sunlight exceeds its shade—the lesser part is nullified by the majority and is therefore as though it were not, and it is called a sukkah on account of the roofing.
If there is a minority of shade, the sukkah is invalid because the majority of sunlight nullifies the minority of shade. According to the commentators, Rashi understands this as the rule of nullification by majority, as in prohibited mixtures, and this raises many questions and difficulties for them.
Beyond this, Rashi’s words here imply that a sukkah in which there is a minority of shade is in principle valid. The problem in a case of majority sun is only that when there is a minority of shade, it is nullified in the majority of sun, and then the minority is regarded as though it were not there. In such a case there is no shade at all in the sukkah, and it is therefore invalidated. This implies that, were it not for the law of nullification, if there were a minority of shade that was not nullified, the sukkah would be valid. If a minority of shade were invalid simply because a sukkah must have a majority of shade (as the plain wording of the Mishnah suggests), then Rashi would have had no need at all to invoke the rule of nullification by majority. He should have said that there is a minority of shade and therefore the sukkah is invalid (even if the shade were not nullified by the sunlight). The point becomes even sharper when one takes into account that Rashi is taking the Mishnah away from its plain sense and using the rule of nullification by majority, whose applicability in such a case is itself far from clear or agreed upon. So why does he do this?
In the Talmudic passage later, on 22b, it becomes clear (according to Rashi’s understanding there) that our Mishnah deals with the sun and shade on the ground, not with the branches and the air above. That is, when the Mishnah here speaks of its sun exceeding its shade, the intent is that on the floor of the sukkah there are more patches of sunlight than shade. The Talmud there explains that even if above there are equal parts branches and air, the sukkah is invalid, because in that state below there will be a majority of sun (for the patches of air in the roofing above grow larger when they are seen as light on the ground).
Several later authorities (for example Kehillot Yaakov, sec. 1, and others) raise a difficulty against Rashi: how can one speak of nullification by majority in a situation where the two components are not mixed together? The roofing and the air are distinct and separate entities, and therefore this is not a mixture at all. In such a case there is no rule of nullification. True, as we saw, Rashi is speaking about the shade and sunlight below and not about the branches and air above, but those later authorities apparently assume that below as well this is the case. The shade and the sunlight on the ground are distinct segments, separate from one another.[4]
What troubles me here is not the halakhic question of nullification by majority, but the perception of reality. For in practice one does not really see patches of shade and sun on the ground. That is not what actually happens in a sukkah. What happens is that there are processes of diffraction, interference, and refraction of light, and below there is some uniform shade of gray. The more air there is above, the lighter the gray, and vice versa. But now another question arises: if the Mishnah is indeed speaking of the sun and shade below on the floor, how can one decide that this gray reflects a situation in which there is more sun than shade, or vice versa? Can a person say that this shade of gray stands exactly halfway between absolute light (= absence of roofing) and absolute darkness (= complete roofing)?
This is in fact a psychophysical experiment, for we are asking people to compare three different states of illumination on the floor of the sukkah: the light in the absence of roofing; the light with complete roofing; and the light in the state under discussion (gray of some intermediate shade). If the gray is of a shade above half illumination, the sukkah is invalid, and if it is less than that, the sukkah is valid. This is literally a comparison between light intensities, and as we have seen there is no way to answer it (and it is doubtful whether it has any answer at all). Of course, we could have taken a scientific measuring instrument and examined the intensity of the electromagnetic field on the floor of the sukkah, but that option was not available to the sages of the Talmud and the medieval authorities (Rishonim). So what, then, were they talking about at all? The criterion for the sukkah’s validity in terms of the illumination of the floor simply does not exist—certainly not on a technical level, and perhaps not even in principle.
Let us illustrate this further. If we use the logarithmic model, then there will certainly be cases in which doubling the field is expressed in only a very small increase in the intensity of light in consciousness (the difference between full illumination and the illumination produced when the roofing covers half the area will be very small, and certainly not double). By contrast, if the model is a power function greater than 1, then even an increase of the light by only a factor of 1.5 may already be perceived as an increase by a factor of 2 or more. In such a case there would in fact be more shade than light, but the observer would see more light than shade (light intensity greater than 1/2), and from his perspective the sukkah would be invalid.
It is important to understand that if the criteria dealt with quantities or areas of roofing as against the air above, the problem would not arise. One can ask what area is covered by roofing as against the area covered by air, and determine which is larger. This is a clear question of physical measurement. But when the discussion is transferred to the hue of illumination on the ground, the question becomes meaningless, or at least unanswerable.
The Geometric Model
There is no escaping the claim that, in order to estimate the intensity of light on the floor of the sukkah, we use a model of geometric optics. That is, we assume that rays of light pass straight through the cracks in the roofing, and the illumination is divided according to the areas formed on the ground. Our estimate of the shade of gray that invalidates or validates the sukkah is based on the ratio of areas in the optical model. Thus, for example, if above in the roofing half the area is covered and half exposed, geometric optics will give us a majority of illuminated area on the floor (this is Rashi’s assumption there, and I will not go into it here). If so, it is true that in practice what we have is a light gray tone over the entire area and we do not know how to determine whether it is closer to full sun or full shade, but a tone produced when the roofing covers half the area is considered in Jewish law to be a tone of majority light (that is, illumination greater than halfway between complete darkness and absolute light). Our inability to assess shades of gray and compare them to one another forces us to use an optical model to estimate this. In this way we have turned a psychophysical question into a question measured by objective tools.[5]
If so, one can perhaps also understand the difficulties raised by the commentators who claim that the laws of nullification by majority cannot be applied here because the components are distinct from one another (there is no mixture). If we relate to the optical model and not to reality itself, then indeed the application of nullification by majority within that framework is problematic. After all, there the assumption is that there are segments of light and shade on the floor and that the sum of the areas of light as against shade is what determines the issue. It may be that the later authorities did not mean this, but rather thought that there really are areas of light and shade on the floor; but in light of this explanation there may perhaps be room for their remarks even from the standpoint of actual reality.
This raises an interesting question about Jewish law in general. Does it deal with reality as it is, or as it is perceived by us (in our consciousness)? But this is not the place to go into that.
[1] On this subject it is worth reading Daniel Algom’s book, Tefisah u-Psikhofizikah (Perception and Psychophysics), in the Open University series. I was first exposed to this fascinating topic through an article in Rabbi Shem Tov Gefen’s book, Ha-Memadim, Ha-Nevu’ah ve-ha-Adamtanut, published by Mossad Harav Kook.
[2] If we are dealing with ratios of intensity and not absolute intensity, alpha of course has no significance. As for ε, it is commonly thought to be a number between 1 and 2.
[3] The question whether there is more or less light is certainly meaningful and has an answer, and usually it can also be answered (and the answers will be fairly uniform). It may be that if someone says of the second state that it has less light, one could say that his perception is defective, and not merely that he uses a different language. But setting quantitative ratios between intensities of light is only a question of language, and perhaps is not defined at all.
[4] The difficulty can of course be resolved in several ways. For example, here it is not really possible to separate the components of the mixture (below) from one another. In such a case, perhaps the rule of nullification applies even if they are each distinct in themselves.
[5] It is important to understand that this is really not far-fetched from the standpoint of halakhic reasoning. From the laws of the roofing in general it is clear that one does not relate to the shade as it actually is, but to some sort of model. After all, in practice the shade on the floor of the sukkah also comes from the walls or from tall objects in the surroundings, and not only from the roofing. The sun, too, is not actually situated directly above the roofing (not even at noon). It is therefore clear that the entire rule of more sun than shade requires a hypothetical optical model in place of empirical reality. We treat the sukkah as though it were situated in an open area and as though the sun were directly above the roofing. Here I have merely added to that model the assumption that there is no diffraction, refraction, or interference of the rays of light—that is, that they pass through the roofing in straight lines according to the laws of geometric optics. All the halakhic calculations are made within this model and not on reality itself.
Discussion
Hello David.
First, I didn’t really understand what your point adds. Only the nature of the function is different in your formulation (I didn’t address that). But I don’t think it is necessarily one-to-one and onto. There could be a person who does not see some color at all, or for whom two different wavelengths are mapped in consciousness to the same color. So the same would also apply between our conscious perceptions.
Regarding the impossibility of “quantification” in the subjective realm:
How can one understand the difference between the possibility of “quantification” and the possibility of saying whether something is “more or less”?
Why do our “subjective tools” allow us only to correlate in terms of “more and less,” but not to measure numerically?
It is hard to define precisely. The feeling is that if in the world there is a stronger field, this ought to be reflected as more light in consciousness. How much more? That is hard or impossible to define. A system that translates more field into less light is a kind of distortion. Though of course that too can be debated.
In most sukkot that I know, one can distinguish on the ground a shadow pattern that reflects very well every little hole in the sekhakh and every branch laid in the sekhakh. At noon it is very easy to distinguish what is shadow and what is not shadow. The claim that everything is gray and only the shade changes is very strange.
Begging your pardon:
A. An acoustic oscillator?! Simply a m i c r o p h o n e
B. The model of physical optics applies to apertures on the order of the wavelength and is irrelevant to gaps of three handbreadths, which are still valid in sekhakh whose shade exceeds its sun.
C. In geometric optics there is no shadow in different shades of gray if the light source is point-like (and the sun, I believe, is point-like for this purpose).
D. With a distant light source like the sun (parallel rays), there is no difference between the light and shadow areas at different distances from the obstruction.
E. A proposal for calibrating the sensation of light: change the light intensity in very small increments and test when people detect a difference. Thus it was discovered that above and below a certain intensity threshold there is almost no sensitivity, and within the sensitivity range there are about 50 levels, where the difference from one level to the next is fairly constant.
model=moda
Forgiven.
A. That too.
B. I didn’t understand the claim. A model belongs wherever one places it. This is not a model that comes to describe reality, but one that comes to give us another way to quantify it.
C. Of course not. Who said otherwise?
D. There is a difference, except that it is small. As stated, the model is qualitative and not quantitative.
E. If I understood, then on your view the relation is linear. But as far as I know, most researchers think it is some other power law. The Weber-Fechner law posits a logarithmic relation, but as far as I know today it is not thought to be correct.
B. You are explaining a geometric phenomenon of shadow by means of a physical phenomenon of diffraction. If there are gray levels and not a sharp shadow, that is not due at all to the sun and the sekhakh.
D. If the rays that left the sun spread apart by one meter over one hundred fifty million kilometers from the sun to the sekhakh, how much will they spread over another meter down to the ground? Completely negligible. In addition, the light and the shadow grow by the same ratio as one moves away from the obstruction parallel to it.
E. Even a logarithm can be linearly approximated in a certain region. It is obvious that it is not linear, because there is saturation.
B. I don’t understand what you want.
D. I cannot explain the same thing a thousand times. The model does not describe reality.
E. ?
This discussion seems bizarre to me. Read again what I wrote.
You convinced me! A perfect article without errors!
Indeed. Perhaps there is an example here of a different perception of reality…
The truth is that even physically I don’t understand where the idea came from that this would happen. For it to happen you need very, very small holes. It does not happen in the macroscopic world.
If you were not convinced, the way to become convinced is to make a Taylor expansion of the logarithm for X=5 around X=1 (as is well known, this is deep within the linear regime). After that one should make such an approximation for all power laws as well, and thus prove that there is no disagreement at all among psychophysicists (except perhaps about the coefficient).
And seriously, if there are mistakes in the article, they are not in physics or mathematics, because I am not claiming anything in that domain. I am once again getting the impression that apparently you did not understand it. All the best.
Check sometime on the ground of your sukkah and see whether you can really see distinct signs of shade and sun there. Perhaps your sukkah (or your consciousness) operates within the model of geometric optics. My sukkah rests on the ground of the world (not on the floor of the model).
Very nice!
I very much enjoyed your rejection of the skepticism in all this. After all, masses of people who are unaware of the difference between reality itself and our cognition of it nevertheless arrive at healthy relationships, wonderful mutual understanding, and an experience free of morbid skepticism. Deepening our understanding of reality is not supposed to destroy our healthy and genuine condition, but to refine it. Someone who is overly clever and ruins a healthy, simple, intuitive experience simply has not understood his own place, or the place of insight, and that there is no contradiction between them at all, only a connection.
I would like to note that apparently it is straightforward from the Gemara itself and from Rashi there that the measurement is geometric, with respect to the shadow on the ground. This emerges from page 22b:
“And if its shade is greater than its sun it is valid. But if they are equal, it is invalid. Yet didn’t we learn in the other chapter: ‘and if its sun is greater than its shade, it is invalid’—which implies that if they are equal, it is valid? This is not difficult: here from above, there from below. Rav Pappa said: This is what people say: like a zuz above is like an issar below.”
And Rashi explained:
“Here from above, there from below—where we inferred that if they are equal it is invalid, that refers to above. When between one reed and another there is a space equal to a reed, even exactly so, it is invalid, because the sunlight from the open air appears on the ground much broader than the shade of the sekhakh. And where we inferred that if they are equal it is valid, the measure was taken below: if sunlight and shade are equal, it is known that the reeds are broader than the open spaces.
Like a zuz above is like an issar below—when the hole is as wide as a zuz, its sunlight below is greater by the measure of a sela.”
And regarding the measure of the quantity of light, I did not understand why it cannot be measured. After all, the measured value has an absolute zero (there is a state of darkness, complete absence of light for our purposes), so why can’t we set up different scales for quantifying the light and its doubling relative to those different scales, such that we can compare the scales?
Hello.
That Rashi is what I was discussing. My claim is that his words do not refer to reality as it is (that is, that on the ground there are distinct patches of light and shadow), but to some model that helps us determine a position regarding it. That is why Rashi allows himself to speak about nullification even though the two components in the mixture are distinguishable from one another (the Steipler’s difficulty).
In this post I used the term “light” to describe consciousness, and the term “field” for the physical phenomenon. That is why I wrote that one cannot measure quantity of light, because that is a measurement of a cognitive magnitude and not a physical one.
Now I understand, thank you.
But why shouldn’t a person be able to estimate a quantity of light intuitively? Such a measurement has some value, especially when it is measured across many people, and if we discover very significant gaps between actual reality and conscious perception, then at the very least we have found something, even if not precisely.
Of course one sees distinct signs of light and shadow, even with a mat, and all the more so with green sekhakh.
If one does not see them, that probably means the holes in the sekhakh are very small, and the sukkah is completely valid.
I am concerned that even your ground of the world is part of the model…
Ah, another possibility is that your vision distinguishes wavelengths much larger than those of most human beings, say microwaves, and they really can undergo interference and diffraction on the scale of holes in sekhakh.
I did not understand the question. I explained this in the article. And even if one can estimate it, that is a subjective measure that does not measure the amount of sekhakh (or the field intensity).
Honorable Rabbi, greetings!
I too have had occasion in recent years to investigate this issue from both the halakhic and the scientific perspectives.
I wanted to note that indeed, as far as I know, there is no diffraction phenomenon in a sukkah (at least not on any significant level). The reason for the gray areas is indeed well explained in geometric optics: the sun is not a point light source, and therefore when the distance between the sekhakh and the floor is great enough, sufficiently wide areas are formed to which only some of the sun’s rays reach.
For elaboration: an article by Rabbi Ben Ezra that appears in the book “La-da’at Ba’aretz Darkekha,” published by Machon Lev
Thanks for the comment. I have no issue specifically with diffraction. The problem is that for various reasons there is gray there, not distinct sun and shade. I mentioned all the phenomena that are being neglected, not necessarily because each one of them is significant.
But a uniform gray is not formed. There are different grays, and one can see the holes in the sekhakh on the floor of the sukkah.
And I still wonder how a PhD in physics can be mistaken about something that even the Sadducees agree on.
Perhaps one can go a bit deeper into the matter:
1) It seems to me that what turns a subjective “thing” into an objective “existent” is its “fixity” and its “persistence.”
Anything whose reality is fixed and unchanging is perceived as objective (existing outside me, not dependent on me),
and without fixity and persistence, everything “found” is perceived as a fiction, as “nothing,” and as not truly existing.
2) “Comparison” sets two existents [fixed ones] opposite one another.
“Measurement” too [which is a certain kind of comparison] sets two existents opposite one another,
except that its content and purpose are to count how many times one “fits into” the other.
That number is what is established as the measure of the thing [as is well known, every measurement is relative].
3) Likewise, in the subjective realm there is no fixity. Therefore the subject does not cognize existents (in the objective sense).
Its grasp is of changing and unstable things [and therefore vague ones].
Therefore every comparison in the subjective realm cannot set a defined and determinate existent opposite another defined existent,
and count how many times one is contained in the other; because in the subjective realm, things “expand and contract.”
At one time it will seem to him that the “large” contains two “smalls,” and at another time it will seem to him that it contains five and a half smalls.
4) The only clear comparison available to the subject is comparing “existents” against absence.
And here one must add that the cognition of absence, which is also a subjective cognition, is not a cognition of infinite absence,
that is, of an absence into which an infinite number of existents can be inserted. It is a cognition of limited absence.
And that makes it possible to correlate and compare between the large and the small, or between the less and the more:
The closer a thing comes to the “maximum” that absence can contain, the greater it is.
Hello,
I did not understand the purpose of all the pilpul about diffraction phenomena when a simple back-of-the-envelope calculation shows that lambda/D for a hole diameter in sekhakh of even 5 mm is 0.0001, which over a sekhakh height of 3 meters translates into an arc of 0.03 cm of diffraction aperture…
It is completely clear that the gray levels are only a linear phenomenon. And the mistake of one of the commenters here is treating the sun as a point source because of its distance. Well, it is indeed 150 million km away, but its diameter (2 million km) gives it a non-negligible angular size in the sky (about half a degree). Therefore it is completely clear that most shades of gray are a linear phenomenon, and to my mind this takes a bit of the sting out of the argument.
On the face of it, the discussion of shades of gray exists in geometric optics as well, and even more clearly so (once the sun is not point-like but has a finite angle).
I came across this by chance, by Heaven, connected to a lesson from today.
A question:
You wrote that the intensity of the light I see cannot be measured; it cannot be quantified. First, this reminds me of your distinction regarding quantity and quality, and here too one could say that the intensity of light is a pure quality that cannot even be quantified. Second, I am wondering about the first question (the technical one) that you asked, “How can one measure the intensity of the light that I see?”—after all, just as the sciences found a tool to measure the heat that I feel (a thermometer), so in the future they may find a tool to measure the intensity of the light that I see?! And according to that, they could also measure whether the intensity doubled or not.
You also wrote, “I am basically wondering here whether such a question is not similar to the question: which is more of an existent: water in the ocean or the good-heartedness of human beings?” But I did not understand: water in the ocean and the good-heartedness of human beings are two different things (it is like asking, what do I have more of: IQ or degrees Celsius), whereas here they are asking whether there is more light A or light B.
See column 99.
I do not think that the intensity of light is a quality. It is a quantity that cannot be measured objectively.
Just as one cannot measure light, one cannot measure heat. Both are subjective sensations. One can measure the body’s degrees, but not what I feel when my body has that temperature. Just as one can measure the intensity of the field that reaches my eye, but not the sensation of light within my consciousness.
“See column 99”? Aren’t we in that column?
Light is definitely a quality and not a quantity; one cannot count light with cardinal numbers, but only (if at all) with ordinal numbers (or say there is more or less light).
As I wrote, the difficulty is not because light is a quality, but because it is subjective (not accessible to measuring instruments).
All right, but why do you say it is a quantity? Light is similar to heat; it is abstract, hard to measure, etc. etc. Instinctively I see it as a quality.
Because in my opinion, in principle there is no problem measuring it; only because it is not accessible to measuring instruments. The number of stars cannot be counted, but it is still a quantity.
Regarding the philosophers’ chestnut, a thought like this crossed my mind:
If we look at each person’s color system, and also its “meanings,” in mathematical terms, then one could say there is a one-to-one and onto function from my set of colors to your set of colors. And also from both sets to the “world of colors” around us. That is, mathematically they function as exactly the same set…