What is the maximum entropy principle?

ChatGPT said:

The maximum entropy principle is a method used to make inferences or predictions in situations where we have incomplete or uncertain information. It is based on the idea that when we do not have full knowledge about a system, the best assumption is to choose the probability distribution that maximizes the entropy, or uncertainty, subject to the constraints that we know about the system.

Entropy in Information Theory

Before delving into the principle, it's important to understand entropy in the context of information theory. In this framework, entropy (denoted as $S$) is a measure of uncertainty or unpredictability associated with a random variable or a probability distribution. It quantifies the amount of "disorder" or the number of possible outcomes in a given system. The higher the entropy, the less we know about the system's state, and the more uncertain we are about it.

Mathematically, for a discrete random variable with possible outcomes $x_1, x_2, \dots, x_n$ and corresponding probabilities $p_1, p_2, \dots, p_n$, the entropy $H$ is given by:

$$H(X) = - \sum_{i=1}^{n} p_i \log(p_i)$$

Where:

• $H(X)$ is the entropy of the system (measured in bits if using the base-2 logarithm),
• $p_i$ is the probability of outcome $x_i$.

The Maximum Entropy Principle

The maximum entropy principle states that when we are uncertain about a system and have limited information, the probability distribution that should be chosen is the one that maximizes the entropy, subject to the known constraints. This principle helps us make the least biased prediction based on the available information, avoiding assumptions beyond what is known.

In other words, the maximum entropy principle is a way of expressing the idea that, without further information, we should assume the least about the system and allow for the maximum amount of uncertainty. This makes it particularly useful when trying to model systems or processes with incomplete or partial data.

Key Features of the Maximum Entropy Principle:

1. Maximizing Uncertainty: The principle suggests that when we don't know specific details about a system, the distribution that reflects the highest uncertainty (entropy) should be used, while still respecting the constraints we do know.

2. Constraints: The constraints often come from the available data or physical laws. For example, if we know the expected value (mean) of a system or the variance, these can serve as constraints on the possible distribution.

3. Least Assumptions: It is the least biased approach to reasoning because it only incorporates what is known explicitly. Any additional assumptions would increase the bias and reduce the entropy (i.e., reduce uncertainty), which is avoided by the principle.

4. Applications in Physics, Statistics, and Machine Learning:

   • In statistical mechanics: The principle is used to derive the statistical distributions that describe the thermodynamic equilibrium of systems (such as the Boltzmann distribution).
   • In information theory: It helps define the most "uniform" or unbiased distribution when we have minimal knowledge.
   • In machine learning and inference: The principle is used in algorithms for probabilistic modeling, such as maximum entropy models, where you seek to find the distribution of data that maximizes entropy given certain observed features (e.g., in natural language processing).

Example: Deriving the Uniform Distribution

Suppose you have a random variable $X$ that can take values in a set $\{x_1, x_2, \dots, x_n\}$, but you don't know anything about the distribution except that all outcomes are equally likely (i.e., no prior information). According to the maximum entropy principle, you should choose the probability distribution that maximizes entropy, subject to the constraint that the sum of the probabilities must equal 1 (since it's a probability distribution).

1. Maximize Entropy:
   The entropy of a distribution $p_1, p_2, \dots, p_n$ is given by:

   $$H = - \sum_{i=1}^n p_i \log(p_i)$$

2. Constraints:
   The constraint is that the probabilities must sum to 1:

   $$\sum_{i=1}^n p_i = 1$$

3. Solution:
   To maximize entropy under this constraint, the solution is the uniform distribution, where each $p_i = \frac{1}{n}$. This gives the maximum entropy because it represents the most uncertain distribution, assuming no further information.

Example: The Max Entropy in Physical Systems

In thermodynamics, the maximum entropy principle is applied to derive the Boltzmann distribution for particles in a gas. If we know the total energy of a system but have no further knowledge about the individual energies of particles, the maximum entropy principle tells us that the most probable distribution of energy among the particles is the one that maximizes entropy, subject to the constraint of fixed total energy.

Applications of Maximum Entropy Principle

1. Natural Language Processing (NLP): In machine learning, particularly in NLP, maximum entropy models are used for tasks like text classification or part-of-speech tagging. Given a set of features (e.g., the presence of certain words in a sentence), the goal is to model the probability distribution of possible outcomes (e.g., word tags or categories) that maximizes entropy while satisfying the constraints defined by the features.

2. Machine Learning and Statistics: The principle is often used in maximum entropy modeling for probabilistic classification. For example, a maximum entropy classifier in machine learning ensures that the model makes the fewest assumptions beyond the observed data and constraints (e.g., conditional probabilities).

3. Ecology: In ecological studies, the principle has been used to predict species distributions in environments with limited data. The maximum entropy approach helps in generating probability distributions that best fit the data without overfitting based on minimal assumptions.

4. Economics and Social Sciences: The principle is also used to infer probability distributions for economic models, social behavior, or other fields where we might have some data (e.g., average wealth, demand) but not full information about the system.

Conclusion

The maximum entropy principle is a powerful concept in statistical inference and various scientific fields, encouraging us to make the least biased assumptions when faced with incomplete information. By maximizing uncertainty (entropy) subject to known constraints, it provides a rigorous method for making inferences about unknown systems, whether in physics, statistics, machine learning, or economics.

Is probability a mathematical artifact or do things literally exist in probabilistic states?

ChatGPT said:

The question of whether probability is a mathematical artifact or whether things literally exist in probabilistic states touches on deep philosophical and foundational issues in both physics and mathematics. There are two main perspectives to consider:

1. Probability as a Mathematical Artefact:

In this view, probability is a tool or construct we use to model uncertainty in systems where we don’t have complete knowledge or where the outcomes are not deterministic. Here, probability is understood as a formal mathematical framework for reasoning about randomness, uncertainty, or likelihood, but it does not imply that things themselves are inherently probabilistic.

• Classical Probability (frequentist interpretation): In this perspective, probability describes the long-run frequency of events occurring in repeated trials. It does not suggest that the events themselves are probabilistic, but rather that the model we use to understand them involves probabilities.

• Bayesian Probability: In this approach, probability is a measure of belief or subjective uncertainty about the state of the world. The probability distribution is a reflection of our knowledge (or lack thereof) about a situation, and the events themselves are not considered to have inherent probabilistic properties.

2. Things Literally Existing in Probabilistic States:

This view suggests that the world, or at least some aspects of it, is inherently probabilistic, and probability is not just a tool but a reflection of the underlying nature of reality. In this interpretation, probability is fundamental to describing the behavior of systems, particularly at microscopic or quantum scales.

• Quantum Mechanics: One of the most well-known examples of this is found in quantum mechanics. In quantum theory, particles do not have definite positions or velocities until they are measured. Instead, they exist in a superposition of states, with the probability of finding the particle in a specific state governed by a probability distribution (the wave function). This suggests that at a fundamental level, particles do not have definite properties until they are observed, and the probabilities reflect this indeterminacy in the system.

• Many-Worlds Interpretation: In the context of quantum mechanics, the Many-Worlds Interpretation (MWI) further posits that all possible outcomes of quantum events actually occur in separate branches of reality, meaning the universe itself splits into multiple parallel realities, each corresponding to a different outcome. Here, the probabilistic nature of quantum events becomes a reflection of the many potential realities that are "real" in a certain sense.

Reconciling the Two Views:

Some interpretations of quantum mechanics, such as the Copenhagen interpretation, suggest that the probabilistic nature of quantum mechanics is a result of the limitations of our ability to measure and know everything about a system. On the other hand, objective probabilistic interpretations (such as the de Broglie–Bohm theory) maintain that probability reflects a real feature of the quantum world, not just a consequence of human ignorance.

Conclusion:

• Mathematical Artefact View: Probability is simply a tool we use to represent uncertainty and model complex systems. Things themselves are deterministic or follow hidden variables we don't know about.

• Literal Probabilistic States: Probability describes a fundamental feature of reality, particularly in quantum systems, where events do not have definite outcomes until they are observed, and the world operates in a probabilistic way.

In the context of quantum mechanics, the idea that things "literally exist in probabilistic states" is widely accepted. However, in everyday macroscopic contexts, it’s more common to treat probability as a way of dealing with uncertainty rather than an inherent property of the universe.

Kaldas

"Descartes’ View of Animals

The moral difference between a puppy and a laptop might seem obvious to us, but it was not at all obvious to the father of modern Western philosophy, René Descartes (1596-1650). Descartes famously thought that animals were merely ‘mechanisms’ or ‘automata’ – basically, complex physical machines without experiences – and that as a result, they were the same type of thing as less complex machines like cuckoo clocks or watches. He believed this because he thought that thoughts and minds are properties of an immaterial soul; thus, humans have subjective experience only because they have immaterial souls inhering in their physical bodies. However animals, reasoned Descartes, show no signs of being inhabited by rational souls: they don’t speak or philosophise, and so (as far as we can tell) they lack souls, and minds. So ultimately, Descartes thought that animals were not hugely different from cars or computers; they were mechanical objects and not living subjects. See his Discourse on Method (1637) and Meditations (1641) for his elaboration of this idea.

Of course, Descartes has been repeatedly and mercilessly criticised for this view, especially in our time, when far fewer people share it. In Descartes’ defence, modern scholars such as John Cottingham have shown that Descartes couldn’t quite stomach his own strict separation of man and beast (‘A Brute to the Brutes’: Descartes’ Treatment of Animals’, Philosophy 53, 1978). Thus, Descartes speaks of animals having sensations, and even feeling emotions like anger and happiness, even though a strict adherence to his dualism would demand that they could only do so if they possessed an immaterial soul. Prevarications like this suggest that, in practice at least, Descartes saw a meaningful difference between animal life and inanimate objects. And it would be hugely unfair to ignore the fact that Descartes had a pet dog, Monsieur Grat, whom he probably loved dearly. But such evidence can only exonerate the man so much. Pets and prevarications aside, Descartes undeniably did set up a strict dichotomy between the immaterial, experiencing, thinking life of man, and the material, mechanical, mindless existence of animals. That dichotomy certainly doesn’t encourage any sense of kinship between man and beast. Rather, it seems to imply that killing a puppy is no worse than spilling coffee on a computer (to take a modern analogy).

Descartes seemed aware that his view absolved us of moral responsibility towards animals. In a letter to the Cambridge philosopher Henry More, Descartes argued: “[My] view is not so much cruel to beasts but respectful to human beings… whom it absolves from any suspicion of crime whenever they kill or eat animals” (reprinted in Penguin Classics’ edition of Mediations and Other Metaphysical Writings, trans. Desmond M. Clarke, 1998). So although this view doesn’t make throwing a puppy over a cliff a good or a wise thing to do, it doesn’t suggest that doing so is particularly wrong.
Cudworth’s View of Animals

A modern reader of Descartes who wanted to refute this view would probably begin by attacking his idea of the soul as the source of subjective experience. Today, we tend to believe that subjective experience arises from the brain rather than from some mysterious non-physical entity. If subjectivity is generated by the brain, then the structural similarities between human and animal brains strongly suggest that animals (and especially mammals such as puppies) have subjective experiences. If animals’ brains give them subjective experiences like ours, then we cannot kill, eat or harm them with total insouciance, as we might scrap an old lamp or a set of headphones that definitely lack that subjectivity.

The response to Descartes I want to look at here though, is not modern. It belongs to a now little-known philosopher called Ralph Cudworth (1617-1688), a younger contemporary of Descartes. Cudworth was an Anglican theologian, a keen Classicist, and for most of his career, Cambridge University’s Professor of Hebrew. Along with the aforementioned Henry More, he was a leading member of a group of philosophers known as the Cambridge Platonists, who promoted the relevance of Platonic philosophy to contemporary life and thought. Although he agreed with Descartes on many things, Cudworth thought (as did More) that Descartes’ view of animals as mindless machines was implausible. For Cudworth, it was clear that an animal is much more like a living, feeling human than an inanimate machine. But Cudworth didn’t think that the similarity between man and beast was purely biologically based, as most of us would argue today. Instead, Cudworth argued that animals, like humans, have souls.

According to Cudworth, Descartes’ mistake was that his conception of the soul was too narrow. Descartes thought that animals’ inability to speak or think reflectively like humans was explained by their not having souls and thus being purely physical machines, but Cudworth saw a problem with this: animals might not speak or reason, but they still do an awful lot. As Cudworth saw it, anyone who can look at the incredible variety and complexity of animal behaviour and decide that it is all merely physical mechanism “will never be able clearly to defend the incorporeity and immortality of human souls” (The True Intellectual System of the Universe, 1678, p.44). In other words, if animals feel and move and communicate as they do purely because of their physical makeup, then there’s no reason to introduce a special, immaterial soul to explain human behaviour. If Descartes is willing to explain the behaviour of all animals as resulting from nothing but ‘blood and brains’, why shouldn’t he draw the same conclusion about us?

For a seventeenth-century Platonist, that’s a surprisingly modern insight; in fact, it’s not unlike the sort of argument many materialists would use to refute Descartes’ dualism today. But Cudworth was not a modern man, and like Descartes, he accepted the orthodox assumption of his time that conscious minds are souls. As we have seen, he was also committed to bridging Descartes’ radical gap between human and animal life. And so, instead of showing that neither animals nor humans have souls, he tried to show that animals have souls too. And although Cudworth thought that animal souls were less perfect and less conscious than human souls, he believed that nevertheless, their existence gives us moral responsibilities towards animals that we do not have towards soulless, mindless objects. So for Cudworth, the specialness of human souls does not entail the worthlessness of animal ones: rather, animals are simply less complex, less developed examples of the same sort of thing that humans are.
Cudworth contra Descartes

Given that today people tend to reject the idea of immaterial souls as outdated, it is tempting to dismiss Cudworth’s talk of ‘animal souls’ completely. If we don’t even believe in human souls, why should we bother with a theory that attributes them to animals too?

Well, for one thing, even if we reject their metaphysical underpinnings, Cudworth’s ideas make for an interesting counterpoint to Descartes’ view; one with important moral consequences. And besides that, I think we will find Cudworth’s concept of the soul much less bizarre once we get to know it better. It is radically different to Descartes’ conception, and you might even say that it has a modern feel. The soul, for Cudworth, is not so much a ‘disembodied mind’ as a kind of life-force that vivifies and animates all life.

However, to understand Cudworth’s concept of the soul as a life-force, we need to first briefly consider Descartes’ dualism, to which it is a response.

Descartes divided all reality into two kinds of things: thinking things (res cogitans) and extended things (res extensa). Thinking things, such as God, angels and human souls, are immaterial and independent of the physical world. Extended things, such as human bodies, animals, plants and inanimate matter, are extended across the three dimensions of physical space. Subjective experience belongs entirely to thinking things, while extended things are nothing but mindless stuff, even if that stuff is intricately formed into clockwork or biological systems.

It is in the context of this strict dualism that Descartes expounds his concept of the human soul. In his Discourse on Method, Descartes concludes that his soul is: “a substance whose whole essence or nature consists only in thinking, and which, that it may exist, has need of no place, nor is dependent on any material thing” (Pt. IV). Thus a human soul is a res cogitans, a thinking thing, entirely independent of the physical world. As a result, Descartes arrives at the idea that the mind or soul is something “wholly distinct from the body” and “would still continue to be all that it is even if the body were destroyed” (ibid). Descartes further believes that in humans, the soul and body mysteriously combine to form a united thing (Meditations, 6.13); but nevertheless, subjective experience belongs entirely to the thinking soul and not to the body. From this, it follows that animals are unlikely to have minds: unless they begin speaking or philosophising, Descartes argues in his letter to More, we have no certain evidence that anything beyond mechanistic, physical motion is occurring in them. And since the mind is an entirely immaterial thing, the mere physical similarities between animals and humans tell us nothing about whether or not animals have minds like ours.

Cudworth, on the other hand, thought Descartes’ dualism was far too presumptuous. He devotes several pages of his ambitiously titled The True Intellectual System of the Universe to showing that Descartes’ concept of the soul does not fit with everyday experience. For one, if Descartes is correct that the nature of the soul “consists only in thinking”, where does it go when we are asleep? When not dreaming, a person in a deep sleep is not expressly thinking anything, just like any inanimate object. In order to maintain that a sleeping person has a soul by his definition of it, Descartes would have to be able to show that people are actually thinking even in the depths of sleep; that the souls of sleepers are “never so much as one moment without expressly conscious cogitations” (TIS, p.160). Otherwise Descartes would be forced by his own definitions to group sleeping people with animals and inanimate objects as purely material mechanisms. For Cudworth, such cases (he provides others; TIS, p.160-1), show that whatever the soul is, conscious thought is not essential to it (and we can reasonably assume, linguistic thought is certainly not).

Considerations like this lead Cudworth to a picture of the soul which is far broader than Descartes’. Rather than a perpetually thinking, immaterial mind, Cudworth indicates his concept of the soul by the various names he gives to it, such as “Life”; “Internal Self-activity”; “Internal Energy”; and even (at his most incomprehensible) “Vital Autokinesie” (TIS, p.159). It is this internal energy that differentiates living creatures – plants, animals, and humans (sleeping or not) – from lifeless matter.

Unfortunately for Cudworth, he founds this idea on an assumption now thoroughly disproven; namely, that all physical motion must be caused by some non-physical substance.

Cudworth thought that matter could not cause its own motion; that it “hath no internal energy, self-activity or life belonging to it” and as such, “is not able so much as to move it self” (TIS, p.163). To explain motion in the physical world, then, Cudworth posited another substance, independent of physical matter, and which must therefore be incorporeal, “which acts upon the matter and hath a commanding power over it” (TIS, p.28). It is this self-active substance, rather than thought or linguistic reason, that makes up Cudworth’s concept of soul. This deals neatly with problem of the sleeping human: a sleeping human might not be thinking, but she still breathes, and her heart still beats; she might even move herself in her sleep. So even if the ‘higher’ part of her soul that causes linguistic thought and reason is currently dormant, this ‘self-activity’ is more than enough for Cudworth to differentiate a sleeping human from a watch or a mannequin.

Cudworth’s assumption that physical matter cannot move itself is, of course, wildly mistaken. We know today that gravity, electromagnetism and chemistry all provide perfectly good physical explanations of motion, including that of plants and animals. But even if we reject Cudworth’s underlying assumption that physical motion must be caused by something non-physical, his idea of the soul as ‘Self-Activity’ is not entirely ridiculous, for it implies a moral distinction that Descartes mostly failed to make: a distinction between living, feeling agents and inanimate objects.

Puppies & Pebbles

In fact, Cudworth’s concept of the soul has two defining features. The first is self-activity – the ability of a thing to determine its own movement and action. The second is subjectivity, which always accompanies the most self-active beings like humans and animals, and even plants to a very small degree. Cudworth argued that in men and animals, the soul creates a “con-sense and consciousness, which makes a being to be present with it self, attentive to its own actions… to perceive it self to do or suffer, and to have a fruition or enjoyment of it self” (TIS, p.159). In simple terms, the more self-active something is, the more aware of its own suffering or pleasure it is, culminating in humans being entirely self-conscious. Even if his underlying metaphysical assumptions are mistaken, Cudworth is surely onto something here: vivid subjective experiences seem to occur only in agents, that is, in highly self-active beings like animals and humans. And in fact, nervous systems did only evolve as organisms became mobile – when they became animals rather than plants.

To see where Cudworth is coming from, compare a puppy and a pebble. Whilst the puppy grows and moves of its own accord, a pebble neither grows nor moves except when it is acted upon by external forces. True, you can’t have a conversation with a puppy (which is crucial for Descartes), but it still seems to subjectively feel things in the sort of way that we do and pebbles certainly do not. Unlike Descartes, then, who must sort puppies and pebbles into the catch-all category of ‘non-thinking things’, Cudworth can point to a meaningful difference between the two: a puppy has internal energy and life in it, which makes the puppy capable of self-activity and subjective experience, whilst a pebble does not. We might not use the same words, but we can’t deny that the puppy is indeed more ‘self-active’ and more a ‘subject’ than the pebble; it has more agency. Even if this has nothing to do with the puppy’s ‘soul’, there is certainly something, or some set of things, which constitute this difference between a dog and a rock. We needn’t stick to Cudworth’s disproven assumptions about an immaterial life-force to get to this conclusion; we could probably find a biophysical basis for the kind of ‘self-activity’ he is talking about it: perhaps it has to do with the sense organs and brain structures that pebbles lack and both puppies and humans have. But the crucial thing is that such ‘self-activity’, whatever it is based upon, allows us to make a meaningful distinction that Descartes did not, between non-human things which are living, feeling creatures and those non-human things which are not. Most importantly, self-activity provides the basis for a meaningful moral distinction between animals and inanimate objects lacking from Descartes’ thought.

The Moral Worth of Animals

To return to where we began: it seems far more wrong to throw a puppy over a cliff than it is to throw a pebble over. If we asked a child why this is so, they would probably respond, “Because a puppy is alive and a pebble is not!” In a way, this is precisely what Cudworth’s ‘self-active soul’ affirms, and what Descartes’ ‘rational thinking soul’ ignores. For Descartes, the defining activity of the soul is (rational) thought, and the only conclusive evidence of thought is speech. In the absence of speech there is no definitive evidence that animals have souls. And because Descartes’ dualism is so absolute, this effectively makes animals and rocks the same kind of thing: both are equally devoid of thought, and therefore they are both equally ‘soul-less’. Our moral responsibilities toward the two will not be radically different. Not so with Cudworth, who has already widened the idea of the soul to include sleeping and comatose humans; that is, to things which are living but which are not thinking. This means that even in the absence of linguistic thought in animals, Cudworth can, and indeed does, recognise a meaningful moral difference between animals and inanimate objects. This becomes clearest at a point in the True Intellectual System where Cudworth examines a famous Scriptural passage about the non-human Creation: “Because Creation itself shall also be delivered from the bondage of corruption… For we know that the whole Creation groaneth and travaileth in pain together until now” (Romans 8:21,22). For Descartes – who was a faithful Catholic – the Creation to be ‘delivered from travail’ is nothing but a senseless, mindless machine. But Cudworth points out, quite reasonably, that mere senseless matter cannot really be in pain in the first place: “In the generations and corruptions of senseless bodies… when for example, oil is turned into flame, flame into smoke… there is, I say, in all this, no hurt done to anything” (TIS, p.866). In other words, there is nothing for senseless matter to be delivered from, because it does not have any subjective experiences. Rather, Cudworth thinks this passage must refer to the parts of the Creation that actually need deliverance from pain; and thus he concludes that God’s New Creation “will not be made for the sake of the senseless matter… but only for the sake of men and animals, the living spectators and inhabitants thereof, that it may be fitter both for their use and delight” (ibid, my emphasis). For Cudworth then, animals are subjects who can experience both delight and pain in the same sense as humans, even though they cannot put those experiences into words. Furthermore, Cudworth’s exegesis of this passage clearly reveals that he saw animal suffering as carrying a moral significance that the destruction of other kinds of matter in motion does not.

Cudworth’s ideas were far more subversive in his time than they might seem to us today. In his intellectual biography of Cudworth, the late John Passmore noted that Cudworth’s philosophy was “regarded with suspicion, as atheistic in tendency” because “he blurred the sharp distinction, on which Descartes insisted, between the human mind and every other sort of natural entity” (Ralph Cudworth: An Interpretation, 1951). In simpler terms, Cudworth noticed and emphasised the animal in the human, and more importantly, the human in the animal; and he did so in an intellectual culture which angrily discouraged such blurring of human-animal boundaries. The result was a moral approach to animals that fits with our moral intuitions far better than Descartes’. For an ancient-minded mystic writing nearly two centuries before Darwin, that’s no small feat''.

© Samuel Kaldas

''It’s not that I don’t understand this whole notion of valuing what we create more than we value what nature creates. When I was a child—and of course now, I’m horrified and ashamed I did this—I loved making terrariums, even caught lizards and snakes to put in them. I dreamt and dreamt of making the perfect terrarium, which would be so large that none of those who lived in it would ever know they were in a terrarium, but still it would be my creation. Never mind that there was a wild world full of lizards and snakes and everyone else already outside my door, with no need for them to be deceived into thinking they weren’t captives, since in all reality they weren’t. So I understand the impulse. What we create and control has value. What nature creates does not. I still like planting seeds, and I pay closer attention to the seeds I plant than I do to the native seeds who sprout in this forest. Likewise, I love putting food scraps into the forest, and watching for when they’re eaten, whether by big creatures, in which case the scraps simply disappear, or smaller organisms, in which case the scraps can take weeks or months to change color, collapse in on themselves, and finally become someone else. And the point is that I get more excited watching this process for the pumpkin scraps I place in the forest than I do for the dried berries hanging on the salal shrubs. The former are my contribution, and therefore special. I understand all this. I also understand that this overvaluing of our own creations and creativity and undervaluing nature’s creations and denying nature’s creativity helps explain many things about this culture. It helps explain how an astronomer can say we need to explore Mars “to answer that most important question: are we all alone?” as this culture destroys life on this planet. It helps explain how so many foresters can continue to claim, as their “forestry” destroys forest after forest, that “forests need management.” It helps explain how people keep trying to “manage fisheries” as they wipe out species after species. It helps explain how even so many so-called environmentalists state explicitly that they are trying to save, not the planet, but civilization, which so many perceive as humanity’s—and thus the universe’s—most important creation. As opposed to perceiving life itself as the universe’s most important creation. Or the universe itself as the universe’s most important creation. Imagine living in a culture sane enough to perceive life on this planet as more important to save (and worthy of saving) than this culture that is killing the planet''.

Jensen

"The use of this work, honoured with a precedent in Aristotle, is nothing less than to give contentment to the appetite of curious and vain wits, as the manner of Mirabilaries is to do; but for two reasons, both of great weight: the one to correct the partiality of axioms and opinions, which are commonly framed only upon common and familiar examples; the other because from the wonders of Nature is the nearest intelligence and passage towards the wonders of art, for it is no more but by following and, as it were, hounding Nature in her wanderings, to be able to lead her afterwards to the same place again."

Francis Bacon

“The Violence of Impediments” Francis Bacon and the Origins of Experimentation By Carolyn Merchant*

Wrestling with Proteus: Francis Bacon and the "Torture" of Nature By Peter Pesic

ChatGpt

 Here are some key points about Haraway's view of the subject:

1. The Subject is Situated and Relational: Haraway argues that subjectivity is never neutral or universal. Instead, it is always situated—shaped by specific historical, cultural, and material conditions. She challenges the idea of a single, objective, or detached subject, instead emphasizing the relational nature of subjectivity. People are always embedded in networks of relations with others, both human and non-human, and these relationships shape how subjects experience and understand the world.

2. Cyborgs and Posthumanism: In her influential work A Cyborg Manifesto (1985), Haraway introduces the figure of the "cyborg" as a metaphor for the blurring of boundaries between human and machine, nature and culture. She suggests that the cyborg, a hybrid of organism and machine, challenges traditional notions of the human subject as separate from technology, animals, and the environment. The cyborg represents the possibility of breaking down rigid boundaries and embracing new, fluid forms of identity that transcend biological determinism and traditional gender roles.

3. Against Essentialism: Haraway critiques essentialist views of identity—those that reduce complex subjects to fixed categories such as gender, race, or species. She emphasizes that identity is socially constructed and dynamic. Instead of focusing on the binary distinctions of male/female, nature/culture, or human/animal, Haraway advocates for recognizing the interconnectedness and complexity of the subject in all its various forms.

4. Situated Knowledge: Haraway also advocates for "situated knowledge," which suggests that all knowledge and perspectives are shaped by the specific positions and contexts of the knower. This contrasts with the traditional view of objective, disembodied knowledge. In her essay "Situated Knowledges" (1988), Haraway argues that knowledge is always partial and shaped by the social locations of those who produce it. Therefore, subjects cannot be understood as neutral or universal; instead, they are always positioned within specific historical and material circumstances.

5. Feminist Subjectivity: Haraway’s feminism also disrupts traditional ideas of the subject. She critiques the ways that women have been historically represented as passive objects of knowledge and instead proposes an active, embodied, and diverse feminist subjectivity. Haraway’s feminist theory focuses on how subjects (women, in particular) are always in conversation with their environments, technologies, and other beings, constantly reconstituting themselves through these relations.

In summary, Donna Haraway's view of the subject is anti-essentialist, relational, and interconnected with both human and non-human entities. She promotes the idea that subjectivity is always "situated," shifting away from universal notions of identity, and calls for new forms of agency and resistance, particularly through the figure of the cyborg and posthuman perspectives.

What happens when human exceptionalism and bounded individualism, those old saws of Western philosophy and political economics, become unthinkable in the best sciences, whether natural or social? Seriously unthinkable: not available to think with. Biological sciences have been especially potent in fermenting notions about all the mortal inhabitants of the Earth since the imperializing eighteenth century. Homo sapiens — the Human as species, the Anthropos as the human species, Modern Man — was a chief product of these knowledge practices. What happens when the best biologies of the twenty-first century cannot do their job with bounded individuals plus contexts, when organisms plus environments, or genes plus whatever they need, no longer sustain the overflowing richness of biological knowledges, if they ever did? What happens when organisms plus environments can hardly be remembered for the same reasons that even Western-indebted people can no longer figure themselves as individuals and societies of individuals in human-only histories? Surely such a transformative time on Earth must not be named the Anthropocene!

With all the unfaithful offspring of the sky gods, with my littermates who find a rich wallow in multispecies muddles, I want to make a critical and joyful fuss about these matters. I want to stay with the trouble, and the only way I know to do that is in generative joy, terror, and collective thinking.

My first demon familiar in this task will be a spider, Pimoa cthulhu, who lives under stumps in the redwood forests of Sonoma and Mendocino Counties, near where I live in North Central California.3 Nobody lives everywhere; everybody lives somewhere. Nothing is connected to everything; everything is connected to something.4 This spider is in place, has a place, and yet is named for intriguing travels elsewhere. This spider will help me with returns, and with roots and routes.5 The eight-legged tentacular arachnid that I appeal to gets her generic name from the language of the Goshute people of Utah and her specific name from denizens of the depths, from the abyssal and elemental entities, called chthonic.6 The chthonic powers of Terra infuse its tissues everywhere, despite the civilizing efforts of the agents of sky gods to astralize them and set up chief Singletons and their tame committees of multiples or subgods, the One and the Many. Making a small change in the biologist’s taxonomic spelling, from cthulhu to chthulu, with renamed Pimoa chthulu I propose a name for an elsewhere and elsewhen that was, still is,and might yet be: the Chthulucene. I remember that tentacle comes from the Latin tentaculum, meaning “feeler,” and tentare, meaning “to feel” and “to try”; and I know that my leggy spider has many-armed allies. Myriad tentacles will be needed to tell the story of the Chthulucene.7

The tentacular are not disembodied figures; they are cnidarians, spiders, fingery beings like humans and raccoons, squid, jellyfish, neural extravaganzas, fibrous entities, flagellated beings, myofibril braids, matted and felted microbial and fungal tangles, probing creepers, swelling roots, reaching and climbing tendrilled ones. The tentacular are also nets and networks, it critters, in and out of clouds. Tentacularity is about life lived along lines — and such a wealth of lines — not at points, not in spheres.

Haraway

What is an eigenform?

ChatGPT said:

An eigenform (or eigenstate in the context of quantum mechanics) refers to a special solution to an equation where the system remains unchanged except for a scaling factor (an eigenvalue). In the context of quantum mechanics, this idea is closely related to eigenfunctions and eigenvalues of an operator, particularly the Hamiltonian operator, which describes the energy of a system.

Let me explain it more clearly:

1. Eigenfunction (or Eigenstate)

In quantum mechanics, the wave function $\psi(\mathbf{r})$ describes the state of a system. When an operator (such as the Hamiltonian $\hat{H}$) acts on a wave function, it often changes the wave function. However, in certain cases, the wave function doesn't change its form, it only gets multiplied by a constant factor. In these cases, the wave function is called an eigenfunction (or eigenstate).

• An eigenfunction $\psi(\mathbf{r})$ satisfies the equation:

$$\hat{H} \psi(\mathbf{r}) = E \psi(\mathbf{r})$$

Where:

• $\hat{H}$ is the Hamiltonian operator,
• $\psi(\mathbf{r})$ is the wave function (or eigenfunction),
• $E$ is a constant called the eigenvalue, which typically represents energy in quantum systems.

2. Eigenvalue

The eigenvalue $E$ is the constant that the wave function is multiplied by when the operator (in this case, the Hamiltonian $\hat{H}$) acts on it. The eigenvalue often represents a physical quantity of the system. For example, in the case of the Hamiltonian, the eigenvalue corresponds to the energy of the system.

In simpler terms:

• The wave function $\psi(\mathbf{r})$ is said to be an eigenfunction of the Hamiltonian if or when the Hamiltonian acts on it, the result is just the wave function multiplied by a constant $E$ (the energy).
• The constant $E$ is the eigenvalue, which represents the energy associated with the eigenstate (wave function).

Example in Quantum Mechanics:

For a particle in a potential well, the time-independent Schrödinger equation:

$$\hat{H} \psi(\mathbf{r}) = E \psi(\mathbf{r})$$

describes the stationary states of the system. Each eigenfunction $\psi(\mathbf{r})$ corresponds to a possible state of the particle, and the eigenvalue $E$ gives the energy of the particle in that state.

Thus, an eigenform in quantum mechanics usually refers to these eigenfunctions (or eigenstates) that describe the possible states of a system, each with a corresponding eigenvalue representing some physical quantity (e.g., energy, momentum).

"Truthfulness has never been counted among the political virtues, and lies have always been regarded as justifiable tools in political dealings. Whoever reflects on these matters can only be surprised by how little attention has been paid, in our tradition of philosophical and political thought, to their significance, on the one hand for the nature of action and, on the other, for the nature of our ability to deny in thought and word whatever happens to be the case. This active, aggressive capability is clearly different from our passive susceptibility to falling prey to error, illusion, the distortions of memory, and to whatever else can be blamed on the failings of our sensual and mental apparatus''.

"Men who act, to the extent that they feel themselves to be the masters of their own futures, will forever be tempted to make themselves masters of the past, too. Insofar as they have the appetite for action and are also in love with theories, they will hardly have the natural scientist’s patience to wait until theories and hypothetical explanations are verified or denied by facts. Instead, they will be tempted to fit their reality — which, after all, was man-made to begin with and thus could have been otherwise — into their theory, thereby mentally getting rid of its disconcerting contingency''.

"The kind of thinking that presents both A and C as undesirable, therefore settles on B, hardly serves any other purpose than to divert the mind and blunt the judgment for the multitude of real possibilities''.

"Not only are the people and their elected representatives denied access to what they must know to form an opinion and make decisions, but also the actors themselves, who receive top clearance to learn all the relevant facts, remain blissfully unaware of them. And this is so not because some invisible hand deliberately leads them astray, but because they work under circumstances, and with habits of mind, that allow them neither time nor inclination to go hunting for pertinent facts in mountains of documents, 99½ per cent of which should not be classified and most of which are irrelevant for all practical purposes''.

"A characteristic of human action is that it always begins something new, and this does not mean that it is ever permitted to start ab ovo, to create ex nihilo. In order to make room for one’s own action, something that was there before must be removed or destroyed, and things as they were before are changed. Such change would be impossible if we could not mentally remove ourselves from where we physically are located and imagine that things might as well be different from what they actually are...It is by no means a matter of course that we can say, “The sun shines,” when it actually is raining (the consequence of certain brain injuries is the loss of this capacity); rather, it indicates that while we are well equipped for the world, sensually as well as mentally, we are not fitted or embedded into it as one of its inalienable parts. We are free to change the world and to start something new in it. Without the mental freedom to deny or affirm existence, to say “yes” or “no” — not just to statements or propositions in order to express agreement or disagreement, but to things as they are given, beyond agreement or disagreement, to our organs of perception and cognition — no action would be possible; and action is of course the very stuff politics are made of''.

Arendt