For many people, the phenomenon of consciousness is the best evidence we have that there must be something important missing in our basic physical description of the world. According to this worry, a bunch of atoms and particles, mindlessly obeying the laws of physics, can’t actually experience the way a conscious creature does. There’s no such thing as “what it is to be like” a collection of purely physical atoms; it would lack qualia, the irreducibly subjective components of our experience of the world. One argument for this conclusion is that we can conceive of collections of atoms that behave physically in exactly the same way as ordinary humans, but don’t have those inner experiences — philosophical zombies. (If you think about it carefully, I would claim, you would realize that zombies are harder to conceive of than you might originally have guessed — but that’s an argument for another time.)
The folks who find this line of reasoning compelling are not necessarily traditional Cartesian dualists who think that there is an immaterial soul distinct from the body. On the contrary, they often appreciate the arguments against “substance dualism,” and have a high degree of respect for the laws of physics (which don’t seem to need or provide evidence for any non-physical influences on our atoms). But still, they insist, there’s no way to just throw a bunch of mindless physical matter together and expect it to experience true consciousness.
People who want to dance this tricky two-step — respect for the laws of physics, but an insistence that consciousness can’t reduce to the physical — are forced to face up to a certain problem, which we might call the causal box argument. It goes like this. (Feel free to replace “physical particles” with “quantum fields” if you want to be fastidious.)
- Consciousness cannot be accounted for by physical particles obeying mindless equations.
- Human beings seem to be made up — even if not exclusively — of physical particles.
- To the best of our knowledge, those particles obey mindless equations, without exception.
- Therefore, consciousness does not exist.
Nobody actually believes this argument, let us hasten to add — they typically just deny one of the premises.
But there is a tiny sliver of wiggle room that might allow us to salvage something special about consciousness without giving up on the laws of physics — the concept of downward causation. Here we’re invoking the idea that there are different levels at which we can describe reality, as I discussed in The Big Picture at great length. We say that “higher” (more coarse-grained) levels are emergent, but that word means different things to different people. So-called “weak” emergence just says the obvious thing, that higher-level notions like the fluidity or solidity of a material substance emerge out of the properties of its microscopic constituents. In principle, if not in practice, the microscopic description is absolutely complete and comprehensive. A “strong” form of emergence would suggest that something truly new comes into being at the higher levels, something that just isn’t there in the microscopic description.
Downward causation is one manifestation of this strong-emergentist attitude. It’s the idea that what happens at lower levels can be directly influenced (causally acted upon) by what is happening at the higher levels. The idea, in other words, that you can’t really understand the microscopic behavior without knowing something about the macroscopic.
There is no reason to think that anything like downward causation really happens in the world, at least not down to the level of particles and forces. While I was writing The Big Picture, I grumbled on Twitter about how people kept talking about it but how I didn’t want to discuss it in the book; naturally, I was hectored into writing something about it.
But you can see why the concept of downward causation might be attractive to someone who doesn’t think that consciousness can be accounted for by the fields and equations of the Core Theory. Sure, the idea would be, maybe electrons and nuclei act according to the laws of physics, but those laws need to include feedback from higher levels onto that microscopic behavior — including whether or not those particles are part of a conscious creature. In that way, consciousness can play a decisive, causal role in the universe, without actually violating any physical laws.
One person who thinks that way is John Searle, the extremely distinguished philosopher from Berkeley (and originator of the Chinese Room argument). I recently received an email from Henrik Røed Sherling, who took a class with Searle and came across this very issue. He sent me this email, which he was kind enough to allow me to reproduce here:
Hi Professor Carroll,
I read your book and was at the same time awestruck and angered, because I thought your entire section on the mind was both well-written and awfully wrong — until I started thinking about it, that is. Now I genuinely don’t know what to think anymore, but I’m trying to work through it by writing a paper on the topic.
I took Philosophy of Mind with John Searle last semester at UC Berkeley. He convinced me of a lot of ideas of which your book has now disabused me. But despite your occasionally effective jabs at Searle, you never explicitly refute his own theory of the mind, Biological Naturalism. I want to do that, using an argument from your book, but I first need to make sure that I properly understand it.
Searle says this of consciousness: it is caused by neuronal processes and realized in neuronal systems, but is not ontologically reducible to these; consciousness is not just a word we have for something else that is more fundamental. He uses the following analogy to visualize his description: consciousness is to the mind like fluidity is to water. It’s a higher-level feature caused by lower-level features and realized in a system of said lower-level features. Of course, for his version of consciousness to escape the charge of epiphenomenalism, he needs the higher-level feature in this analogy to act causally on the lower-level features — he needs downward causation. In typical fashion he says that “no one in their right mind” can say that solidity does not act causally when a hammer strikes a nail, but it appears to me that this is what you are saying.
So to my questions. Is it right to say that your argument against the existence of downward causation boils down to the incompatible vocabularies of lower-level and higher-level theories? I.e. that there is no such thing as a gluon in Fluid Dynamics, nor anything such as a fluid in the Standard Model, so a cause in one theory cannot have an effect in the other simply because causes and effects are different things in the different theories; gluons don’t affect fluidity, temperaturs and pressures do; fluids don’t affect gluons, quarks and fields do. If I have understood you right, then there couldn’t be any upward causation either. In which case Searle’s theory is not only epiphenomenal, it’s plain inaccurate from the get-go; he wants consciousness to both be a higher-level feature of neuronal processes and to be caused by them. Did I get this right?
Best regards,
Henrik Røed Sherling
Here was my reply:
Dear Henrik–
Thanks for writing. Genuinely not knowing what to think is always an acceptable stance!
I think your summary of my views are pretty accurate. As I say on p. 375, poetic naturalists tend not to be impressed by downward causation, but not by upward causation either! At least, not if your theory of each individual level is complete and consistent.
Part of the issue is, as often happens, an inconsistent use of a natural-language word, in this case “cause.” The kinds of dynamical, explain-this-occurrence causes that we’re talking about here are a different beast than inter-level implications (that one might be tempted to sloppily refer to as “causes”). Features of a lower level, like conservation of energy, can certainly imply or entail features of higher-level descriptions; and indeed the converse is also possible. But saying that such implications are “causes” is to mean something completely different than when we say “swinging my elbow caused the glass of wine to fall to the floor.”
So, I like to think I’m in my right mind, and I’m happy to admit that solidity acts causally when a hammer strikes a nail. But I don’t describe that nail as a collection of particles obeying the Core Theory *and* additionally as a solid object that a hammer can hit; we should use one language or the other. At the level of elementary particles, there’s no such concept as “solidity,” and it doesn’t act causally.
To be perfectly careful — all this is how we currently see things according to modern physics. An electron responds to the other fields precisely at its location, in quantitatively well-understood ways that make no reference to whether it’s in a nail, in a brain, or in interstellar space. We can of course imagine that this understanding is wrong, and that future investigations will reveal the electron really does care about those things. That would be the greatest discovery in physics since quantum mechanics itself, perhaps of all time; but I’m not holding my breath.
I really do think that enormous confusion is caused in many areas — not just consciousness, but free will and even more purely physical phenomena — by the simple mistake of starting sentences in one language or layer of description (“I thought about summoning up the will power to resist that extra slice of pizza…”) but then ending them in a completely different vocabulary (“… but my atoms obeyed the laws of the Standard Model, so what could I do?”) The dynamical rules of the Core Theory aren’t just vague suggestions; they are absolutely precise statements about how the quantum fields making up you and me behave under any circumstances (within the “everyday life” domain of validity). And those rules say that the behavior of, say, an electron is determined by the local values of other quantum fields at the position of the electron — and by nothing else. (That’s “locality” or “microcausality” in quantum field theory.) In particular, as long as the quantum fields at the precise position of the electron are the same, the larger context in which it is embedded is utterly irrelevant.
It’s possible that the real world is different, and there is such inter-level feedback. That’s an experimentally testable question! As I mentioned to Henrik, it would be the greatest scientific discovery of our lifetimes. And there’s basically no evidence that it’s true. But it’s possible.
So I don’t think downward causation is of any help to attempts to free the phenomenon of consciousness from arising in a completely conventional way from the collective behavior of microscopic physical constituents of matter. We’re allowed to talk about consciousness as a real, causally efficacious phenomenon — as long as we stick to the appropriate human-scale level of description. But electrons get along just fine without it.
Logicophilosophicus,
I understand the laws of thermodynamics as well as anyone. You should read up on entropy in terms of information theory.
Think about it this way. Given a starting condition of unmixed cream and coffee, it is SIMPLE to make a uniform mixture of the two. But, given a starting condition of mixed cream and coffee, it is VERY COMPLICATED to make unmixed cream and coffee.
Unlikely states have low entropy. Likely states have high entropy.
Why should I be embarrassed?
I will try to be a bit more clear.
The 3rd law of thermodynamics has basically nothing to do with mixed liquids.
In an infinite perfect crystal at zero degrees, every atom ‘knows’ exactly its orientation and position relative to every other atom in the crystal. This is zero entropy.
With a mixture of water based liquids at 50 degrees, the closest you will ever have to a perfect crystal is two non-mixed layers.
Moe
You wrote:
“The highest entropy describes the simplest state… The lowest entropy describes the most complex state.”
Sean Carroll wrote:
” So I don’t think downward causation is of any help to attempts to free the phenomenon of consciousness from arising in a completely conventional way from the collective behavior of microscopic physical constituents of matter. “.
As an atheist, its evident you propose that conscience comes from matter.
That is nonsense, for good reasons.
Einstein’s Gulf: Can Evolution cross it? by John Oller, Ph.d
http://reasonandscience.heavenforum.org/t1283-einstein-s-gulf
Albert Einstein,undoubtedly one of the greatest scientists of all time, described the “gulf’ that logically separates the concrete world of hard objects on the one hand from the abstract world of ideas on the other. He wrote: We have the habit of combining certain concepts and conceptual relations (propositions) so definitely with certain sense experiences that we do not become conscious of the gulf-logically unbridgeable which separates the world of sensory experiences from the world of concepts and propositions
On the one side, we find the real world of objects, events, and tensional spacetime relations. On the other side, we find fully abstract representations that contain information about the material world. That articulate information is abstracted first by our senses, secondarily by our bodily actions, and tertiarily by our ability to use one or more particular languages . Between the two realms we find what appears to be an uncrossable gulf.
A small part of the materialists problem is that hard objects are never observed spontaneously to transform themselves (on their own recognizance) into abstract ideas.
Max Planck, theoretical physicist who originated quantum theory, which won him the Nobel Prize in Physics in 1918
“I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.”
Eugene Wigner, theoretical physicist and mathematician. He received a share of the Nobel Prize in Physics in 1963
“It was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to consciousness.”
R.C. Henry, Professor of Physics and Astronomy at Johns Hopkins University , “The Mental Universe” ; Nature 436:29,2005) ? He wrote:
“A fundamental conclusion of the new physics also acknowledges that the observer creates the reality. As observers, we are personally involved with the creation of our own reality. Physicists are being forced to admit that the universe is a “mental” construction.
Pioneering physicist Sir James Jeans wrote:
“The stream of knowledge is heading toward a non-mechanical reality; the universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter, we ought rather hail it as the creator and governor of the realm of matter. Get over it, and accept the inarguable conclusion. The universe is immaterial-mental and spiritual.”
Sir Arthur Eddington explained:
“It is difficult for the matter-of-fact physicist to accept the view that the substratum of everything is of mental character.”
Newton called light “particles”, knowing the concept to be an ‘effective theory’ — useful, not true. As noted by Newton’s biographer Richard Westfall:
“The ultimate cause of atheism, Newton asserted, is ‘this notion of bodies having, as it were, a complete, absolute and independent reality in themselves.’” Newton knew of Newton’s rings and was untroubled by what is shallowly called ‘wave/particle duality’.
Moe,
Both the lowest and highest entropy states are the simplest. The most complex state is in the middle of the two extremes.
Take my crash course on ‘Mechanics and Thermodynamics’ at link below (58 wiki articles A-Z):
http://www.zarzuelazen.com/Mechanics.html
Cheers!
Moe
Let me make you a very small cup of iced coffee. The upper layer contains 5 molecules of lipid which we assume are identical, and the lower ditto caffeine. Chill it to 0K. OK?
We scan the unmix according to some scheme, and the arrangement is LLLLLCCCCC with no alternatives.
Heat, stir, refreeze. Repeat ad lib.
We scan the mix after each refreeze, and find hundreds of different arrangements. (I suppose 10!/5!) The unmix had a very small information content, and therefore low entropy. The mix has a much larger information content, and therefore much higher entropy. That’s what we expect. Each refreeze follows an input of energy, which inevitably increases disorganization-entropy. The refreeze is a snapshot of the continual thermal reshuffling of the molecules. Entropy is a measure of disorganization.
You may have been reading some theoretical cosmology, where the vast entropy of our post-Big-Bang universe is diluted – possibly infinitely – by the vastness (infinite?) of space. Cosmologists may or may not be able to draw some clever conclusions from these suppositions, one of which is that the entropy density becomes tiny (zero?); but ENTROPY DENSITY does NOT equal ENTROPY.
Is high information a corollary of high disorganization/disorder?
I think this is a question of confusing high level narrative.
A string constrained as 5 1’s followed by 5 0’s is a very low entropy message. You can’t send any information with it (unless you play with the bit rate and/or amplitude). The same length, 10-bit sequence, permitted to be any possible sequence containing 5 1’s and 5 0’s, has a higher entropy, or unpredictability, and it can define a very particular state among many others. It therefore has the potential to carry more information. Its potential, as a message, to bring order into a situation is higher. Here we normally have exact knowledge of the microstate.
In a liquid mixing scenario, we could argue that the most ordered state is the 1111100000, or LLLLLCCCCC, because it looks specific, and because among the general sequences it stands out clearest. For a stirred beverage, the exact microstate is not of concern, and the beverage would be considered disordered in most cases. (Especially if you are English like me and ordered tea.)
Indeed, for digital electronics to work at all, we need to be able to guarantee a low-entropy charge population state in every individual potential well so we can tell whether we are storing a one or a zero state.
‘Unlikely states have low entropy. Likely states have high entropy. ‘
True for states = macrostates. Unlikely or unique macrostates have low, or zero, respectively, entropy.
I’m starting to see how it might be possible to close the ‘ontological gap’ between matter and consciousness! The key to it is time!
There are two ways we can try to ‘close the gap’ (between mind and matter). We can start from the bottom (matter) and move *up* the complexity hierarchy. We can also start from the top (mind), and move *down* the complexity hierarchy. If we can get to a level of description (or vocabulary) where the two will meet in the middle we will have done it – we will have solved consciousness!
So lets try .
Bottom up from matter –moving to higher-levels of emergence
Particle physics (fields) > Mechanics > Space and arrow of time emerging
And top-down from mind –breaking the concept down to lower-levels
Axiology (values) > Decision and Game Theory > Cognitive Psychology > Executive functions > Working Memory > Imagination and Memory > Time perception (past-present-future)
The gap between mind and matter has really narrowed! Look:
Matter>>Arrow of time at top level>>LINK!<<Time perception at base << Consciousness
The gap is almost closed! And it’s clear that ‘time’ is the link!
correction to my last post.
Unlikely or unique macrostates have low, or zero, respectively, entropy.
I mean microstates, of course.
SP
The key word is “constrained.”
If 1111100000 is constrained, it carries no information and has low/zero entropy and is extremely likely (p=1).
If 1111100000 is observed as an outcome of random shuffling, then it carries the same 7 or 8 bits of information about the system state as every other permutation, has maximum entropy, and maximum unlikeliness.
If 1111100000 is a message in some language, we can’t state how unlikely it is until we know enough about the language. For example, suppose the pretransmission code 01 means “detonate the bomb” and 10 means “disable the bomb”. The controllers of the agent have very wisely decided to build in five-fold redundancy, to allow for signal corruption. Receiving 1110100001 the agent may still confidently dismantle the bomb. In this case 1111100000 carries a single bit of information. Shannon information is user-dependent and is a dangerous model when casually applied to thermodynamic processes. Blame von Neumann for that.
Simon Packer,
“I think this is a question of confusing high level narrative.”
Of course.
As I said a while ago in this comment thread, entropy is only meaningful when lots of states are possible (macrostates only), and if there is also a way to distinguish those states.
When rolling a single die, no entropy is involved. No statistics are necessary. When rolling two dice, entropy is involved IF you can’t tell the difference between ‘2+5’ and ‘3+4’. This is when statistics emerge, along with entropy issues.
The world we live in is dominated by entropy.
So… we must not be able to distinguish between some basic levels of physics that appear identical to us, but are actually different things.
We can’t see the dice, only the sum of the numbers.
Moe
Roll a die. Don’t look yet. Does a peek – a “measurement” – give you any information about the state of the system?
Logicophilosophicus:
Actually, yes. If you only look at one corner and see a dot, you know it can’t be an one but it could be any other number. If you don’t see a dot, you know it can’t be a four, five, or six.
And if you can’t get a clear picture from an individual corner, you still might be able to build a statistical model based on average corner brightness.
Cheers,
b&
Point agreed…thermodynamic and Shannon entropy are substantially different conceptually, in particular regarding the way they might be seen to embody the concept of information.
A low thermodynamic or quantum entropy state appears ordered to us and can easily be used to convey information. It does so (in the case of a binary system) by contrasting with another low entropy condition (or with a high entropy condition). Has your latte been stirred? 1 Shannon bit of information. The states are chosen to be easily identifiable/measurable. For a semiconductor memory by measuring potential difference across a charge well. Here the Shannon entropy is much lower still than the likely thermodynamic or quantum entropy.
An example of a zero Shannon entropy situation would be a contiguous data system constrained to a particular repeating sequence. In my example I chose the digital equivalent of your un-stirred 10-bit nano-latte. We might call it ordered, but it can carry no information in a contiguous, non-frame aligned, phase-coherent system.
Starbucks opened in Cape Town, I wonder if they do them. 10-bit nano-lattes.
Moe/Ben
When I wrote “peek” I meant “look at the number”. Now you know the number is (say) 5, but I and everyone else only know that it is 1, 2, 3, 4, 5 or 6. You could reduce my state of uncertainty by sending me a message which would require 3 bits. You are in possession of information, and the system (you + die) is complex. That is EXACTLY the kind of system Planck discussed – a SINGLE particle with a number of possible states (or, as it is often put, a conceptual space containing six possibilities). You absolutely do not need multiple particles to apply statistical mechanical reasoning. Reading the actual value on the die is a measurement corresponding to a reduction of a complex state function. That is why QM is intrinsically “thermodynamic”.
SP
The concept of “order” is the awkward part – and is the basis for the trickiness of Shannon Information in relation to language. If we define a scanning (or encoding) procedure we can in principle list any state of any system as a single list of 1’s and 0’s. (I believe Poincare showed that even if the values of variables are infinitely divisible, this can be done to any requuired degree of accuracy by choice of scale.) Every list is ordered. When we talk about order we actually mean something else, related to constraint. In biochemical systems Leslie Orgel named this “specified complexity” but it is implicit in Shannon Information theory. A sequence of x binary digits CAN encode x bits of information, but that is not the same as saying that it DOES. We need to be aware of what (if anything) is “specified”. If I send a message corresponding to the text of Hamlet, it is the existence of the text – that prior copy of the same information – which specifies the message.
We are a binary system, between the central nervous system processing information/form and the digestive, respiratory and circulatory systems processing energy. Life is, as they say, the journey, not the destination.
So rather than totally obsess over the form, i.e.. the information, some consideration should be given tot he process, the actual energy doing the stirring. These forms come and go, but the stirring continues.
The energy radiates from past to future forms, while these forms coalesce into ever more dense and ordered structures, but to do so, radiate away excess energy. Thus going future to past.
Given the direction of order is to express more with less, then the ultimate ideal of order would be to express everything with nothing. So we get to black holes. Everything falls in and only energy radiates out. Leaving galaxies as cosmic convection cycles, of coalescing structure and radiating energy.
So when you have abstracted everything down to a dimensionless point, turn around and consider all that had to be discarded in order to do so.
We are linear, but nature goes in cycles. Complexity is all the swirls and eddies in the middle somewhere, between static form and chaotic energy.
Consciousness is energy, going past to future, while thoughts are form, going future to past.
“That is EXACTLY the kind of system Planck discussed – a SINGLE particle with a number of possible states (or, as it is often put, a conceptual space containing six possibilities). You absolutely do not need multiple particles to apply statistical mechanical reasoning. Reading the actual value on the die is a measurement corresponding to a reduction of a complex state function.”
Why isn’t the quantum mechanical 6-sided die coming up equally between the six states when I repeat the experiment many times? Instead, we get a distribution.
The states that we get to call ‘a measurement’ must be the result of multiple dice, not just one die. We don’t get to read them seperately. The peek we get is that a black box with dice inside displayed the total. We don’t even know how many dice are inside this box.
And it looks like different readings are related in certain orthogonal ways.
Let’s say you dropped 2 dice into two slots that allowed you to either read the top or the side, but not both at the same time. If you got a great look at the result of the sum seen on the top each roll, you could make a distribution of outcomes that would make a bell curve. The same if you only had a sum from the sides.
However, you can never see both types of results for one roll. The fact that you know the result for the top view gave you zero information about the side view. It could have been anything. You can make statistics, but you can never give a definite answer.
JM
“The conservation of energy is a little more difficult, because this time we have a number which is not changed in time, but this number does not represent any particular thing… It is abstract, purely mathematical…” Feynman (The Character of Physical Law). If you want to add a new form of energy (consciousness) then it had better be in very minute quantities, otherwise the known forms would not show strict conservation. But, in any case, how do you arrive at such a conclusion? Where is the quantitative evidence? How does it fit into Feynman’s (or anyone else’s) “purely mathematical” equations? Your answers to life, the universe and everything are vague to the point of meaninglessness. For example, suppose I define (as I do) consciousness as the succession of “ideas” (perceptions, emotions, reflections, volitions): could you please give me a hint of what consciousness feels like WITHOUT such thoughts/ideas, as must be possible in your theory?
Moe
“Why isn’t the quantum mechanical 6-sided die coming up equally between the six states when I repeat the experiment many times? Instead, we get a distribution.” Which QM die? Which distribution? For illustrative purposes I discussed a rolling die coming to a halt on a flat surface as a system governed by a probability distribution of six equiprobable states. It’s an analogy. If you insist on talking about some other thing, tell me what it is?
“The states that we get to call ‘a measurement’ must be the result of multiple dice, not just one die.” Only if you insist on putting an s on the end of “state”. I only discussed one ideal die, as just re-described.
“We don’t even know how many dice are inside this box.” I know there’s only one in my case (as re-described…) Where is this box with an unknown number of dice?
And it looks like different readings are related in certain orthogonal ways.
“Let’s say you dropped 2 dice… you could make a distribution of outcomes that would make a bell curve.” Actually not – there’s that infinity thing again. You would get “closer and closer” approximations, as the number of trials became very large, to n/36, 2n/36… (the 1,2,3,4,5,6,5,4,3,2,1 pattern) if you were taking the sum as the measurement.
Logico,
I’m not so much saying consciousness is an energy, as I’m saying its relationship to thought is similar to the relationship of energy to forms/events. You hit a ball and as the energy is transferred to the ball, the event and form of you hitting it recedes into the past, while the ball flies away, transmitting the energy. Just as your consciousness is constantly perceiving information and distilling thoughts from it, such that the information and subsequent thoughts, as forms, recede into the past, while the state of your consciousness proceeds onto further thoughts.
I could list any number of ways how this relationship exists. For instance, in the dynamic of life, individuals are being born, living and dying, thus going from being in the future to being in the past. Meanwhile the process of life is constantly moving onto new generations and shedding old ones.
Consider a factory, in which the product goes from start to finish, thus future to past, while the production line points the other direction, consuming raw material and expelling finished product.
In these examples, say building a car, for example, enormous amounts of raw material, iron ore, silicates, petroleum products, etc. are being pulled into the process and much of it is either distilled away, or channeled in other directions, before the particular entity of the car emerges. Then the profits and wages generated through the subsequent sale of these vehicles and subsequent energy required to propel and maintain them.
Not to mention how much resources go into providing for the physical and environmental care and feeding of people.
So, to reiterate the cycle, structure and form coalesce, radiating away energy in the process and eventually all of the energy is shed, from cars rusting away and people dying, to black holes radiating away everything from the initial light being shed by stars, to the cosmic rays being ejected from the poles, to enormous gravity waves, as black holes combine into bigger, more efficient black holes. Meanwhile this energy dissipates, eventually to start coalescing again, as subsequent forms and events.
Form and energy. Can’t have one without the other. The difference is opposite directions of time. Energy goes from prior to succeeding forms, as these forms come into being and dissipate.
As for math, it is abstraction; Order from chaos. Signal from the noise. If you don’t have some dynamic creating the noise in the first place, there is no signal.
Factors are form, while functions are process. Like the factory going from raw material to finished product, equations process factors according to functions, in order to get solutions. Many are repetitive, but as Wolfram said, it would take a computer the size of the universe to compute the universe.