I am not sure where the connection between group theory and the ultimate theory of physics comes from. Mathematics involves concepts beyond groups (mathematical fields, rings, etc.), so this connection would seem to be too simplistic (especially if science builds off of mathematics).
More importantly, the Monster Group is limited to Real numbers, when we already know of complex numbers. Part of mathematical progress is extending existing concepts over additional domains (polynomials with integer co-efficients and positive exponents; polynomials with rational or real co-efficients; polynomials with rational, negative, and real powers - groups and fields over the integers, over reals, etc.) Since we are still working on expanding to the complex numbers, I think there is space for quite a bit more new mathematics, upon which newer science can be built.
Can Science be different? Maths says "NO'
Charles St Pierre
RE “But here's a speculation for you: Is the Monster Group the most complicated thing, or at least sets the limit on, the most complicated thing, which can exist?”:
There is no connection between group theory and physics. The only real-world numbers that could be said to exist are the numbers obtained from measurement of (e.g.) relative position or mass. The Monster Group is not the most complicated thing that can exist, simply because it doesn’t really exist at all, except in the human imagination, like fairies at the bottom of the garden.
Myrtle Coral concludes: “Thus we can conclude that our science, its evolution, its philosophy, its institutionalization, etc. are deterministic, and cannot be different from what we have seen. As far as we know, the universe is built of the same 'stuff' as we are, and so the science and the path of evolution of science will be the same for any aliens.”
I would argue that consciousness trumps determinism, and as a consequence the path of evolution of science can be different, and will be different when we meet other galactic aliens.
I previously commented that Lovelock and Margulis developed a hypothesis they called Gaia, in which living organisms interact with their inorganic surroundings on Earth to form self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.
I wonder if Gaia could be part of the Universal consciousness? Could it extend to whole galaxies as well? And I suggest that with faster than light communication a universal “being” may be possible.
Lorraine Ford There is no connection between group theory and physics.
So I think your assertion needs supporting evidence. Or proof. Which ever is more convenient for you. Until then it is more of a- speculation, unsupported by fact.
Charles St Pierre
I'm saying (in my essay) that numbers have no inherent category, i.e. numbers have no inherent relationship to anything else in the physical world, therefore they don't and can't exist. I'm saying that the only numbers that can actually, physically, be said to exist are the numbers that are associated with a genuinely existing, measurable, physical category like relative position or mass. Other than that, and having studied mathematics, I'm quite happy to say that numbers and groups, and indeed most of mathematics, are merely a figment of the human imagination. The human imagination is interested in relationships between things, hence mathematics. The world is built out of genuinely existing relationships between things, hence physics.
Physics is about a world that actually exists. It is not up to me to prove anything, it is up to you to explain what is the difference between what actually exists in the world/ universe, and what only exists in the human imagination.
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Lorraine Ford Physics is about a world that actually exists. It is not up to me to prove anything, it is up to you to explain what is the difference between what actually exists in the world/ universe, and what only exists in the human imagination.
@[deleted]
Naturally, intelligent creatures with
incredibly powerful neural network may not exist. So the evolution of science will always
be a slow process, as has happened in our case, and cannot be instantaneous
while preparing to write this comment a few hours ago, focusing on the essay abstract i had the idea that math is at the base/bottom of everything. and the same moment i picked up a glass to fill it with water and the small plate that was standing on, surprisingly, it was temporarely glued .maybe there could be a /science that isn't dependent on mathematics at least not the way people know it , considering other kinds of brains
imagine an alien that cannot forget anything and has some kind of a brain that grows continuously and layers of recent memories are being dropped like shells of a crab /snake tree/ , thick dead "neural memory skin"at the sensory place / head level, and other of the same species can pick those shells and relive it
an other kind is like, to make a comparison, learning the contemporary math for a differently alien species could be like the supporting scaffold for 3d plastic wire printing that is being removed, ( or something similar for liquid concrete ) a something that is for support in the process of building, not at the finished product
an other idea was crossing my mind the monster group , how could such thing be made ,to be a physical thing
aa aaa aaaaa ... aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
here is an example of simple trace for the monster group embeded in the screen that you detect in the dark/lightening up pixels, the row above
@[deleted]
the wavefront might be irrelevant in considering large amounts of time in the short run there are bumps that go faster or slower.
a layer that is missing depth is the layer of how this mathematics is practiced , language is obvious and invisible, not like a deaf language where also space play a role
Lachlan Cresswell Well, consciousness, which necessarily contains some system of self-stabilizing and self-reinforcing internal feedback loops, can certainly engender chaos, which we find to be often unpredictable. However, the standard definitions of consciousness, while flattering, are much to narrow. And misleading. It is these definitions which precludes the existence of the likes of Gaia. Or God.
We have defined consciousness so that these types of entities cannot be conscious. These forms of consciousness, of experience, will not fit into the box of our standard definitions.
Lorraine Ford A brick is a brick. It does not matter what we think a brick is. A materials scientist, an architect, a bricklayer, a footpad, all have different ideas, different understandings of what a brick is. But a brick is what it is, Our definitions, our ideas, our understandings, can only be less than the reality.
And for many subjects, our definitions may not be faithful representations of the reality, and so may mislead. And a construct made of unfaithful definitions will itself be unfaithful, (I think, That may require proof. But it seem most likely.) This reminds me of a Zen parable. So the master of this (Zen, I suppose) temple was getting along, and thinking about spending more time in contemplation in the tea house out behind the temple, and so decided the temple would require a new master to replace him. So to figure out who might be the best replacement, he brought all the monks of the temple together. He explained he was retiring to spend more time in contemplation, or whatever, and their temple would need a new master. He then placed a pitcher of water on the ground before all of them, and announced that who ever best described the water in the pitcher, he would name as his successor. So one after the other the monks came forward, sat before the pitcher of water. They sat and spoke of all the qualities of water, all the meanings of water, they could think of. All the things that water meant to them. One after the other, until the temple cook, in disgust, and amusement, walked up to the pitcher and kicked the pitcher over. (Editorial liberties taken.) Anyway.
So the point here is that math is what it is. Our definitions of math cannot be the whole of math, and they can be, and most likely are, unfaithful representations and misleading.
Let me offer you a description of a different system of defining numbers:
"It is an undeniable fact that any given number is not just one more than the previous number and one less than the subsequent number, but is an independent individual idea, a thing in itself; a spiritual, moral and intellectual substance, not only as much as, but a great deal more than, any human being. Its merely mathematical relations are indeed the laws of its being, but they do not constitute the number, any more than the chemical and physical laws of reaction in the human anatomy give a complete picture of a man." The Book of Thoth, Aleister Crowley. (1944)
So Crowley and other people of similar inclination, before and after, sort of ended up trying to develop number theory from a phenomenological point of view, and with out actually knowing much number theory. And maybe too much religion. Anyway,
The Western Mystical Tradition is a (relatively recent) offshoot of Jewish Kabbalah, which goes at least hundreds and maybe thousands of years to the original formulations of Jewish Kabbalah and Jewish mysticism, where these associations between numbers and phenomena were first (attempted to be) worked out.
While it is important to be consistent in one's definitions, it is also important not to try to fit realities into the boxes of your definitions, For an instance of practical application, the definition of 'money' as used by economists is a bad one, It is unfaithful to the reality of money,* and will contribute to the collapse of Techo-civilization.
*And so money is also an unfaithful representation of economic activity and value, (vs market value,) In consequence, economic activity increasingly turns away from useful production and activity as inequality increases. The demand for luxury by the few out weighs the demand for necessity by the many, and by the productive economy itself.
More properly, money is not an asset. It is demand on assets. So, for example if you have $100 dollars, that is not really an asset. Yes, you can take your money to the grocery store and buy $100 worth of food, real assets you can store in your refrigerator.
But you cannot eat the money. While on a _micro_economic scale money can act like an asset, on the _macro_economic scale, one can see that the quantity of money does not add anything to the value of an economy. Money is not food, it is not fuel. It is not a factory. Or a store or a house. It is demand on the real things an economy produces. OK. So.
Don't throw out the baby with the bullshit.
Charles St Pierre
A number is not like a brick which you can weigh and measure, and which has a position relative to something else; a brick exists in genuine relationship to the rest of the physical world. In the real measurable physical world, a number is the result of measuring a category (like mass or position). You can’t weigh or measure a number itself, and the reason is that a number itself has no inherent category.
In the human imagination, numbers seem to have a category, which would seem to be “the number category”. But in the real measurable physical world, outside of the human imagination, numbers only exist in association with a category, which are things that only exist in relationship to other such categories.
I was pleased you referred to arithmetic, and agree, apparently from first hand experience, that Alien Physics will be different, but apparently not just as physical properties differ. You write; "Even an omnipotent creator cannot defy the laws of arithmetic, nor can he create any new arithmetic." But have you considered that we may not be correctly using numbers to model the processes of nature?
As an example I give the infinite hierarchical structure of propositional logic as entirely following the infinite hierarchical structure of the rules of brackets. Those aliens seem convinced that what we call 'IRF's' are entirely equivalent to bracketed functions, so 'c' can only be valid and computed INTERNALLY. Only a final 'product' can then be computed with the 'next function out' in the 'sub-proposition' sequence, or brackets. I found that works perfectly, (so do the aliens, who also identify other 'incompletions'!) but it's NOT as current doctrine!
Nice essay, well argued, but is it entirely a complete argument?
Donald Palmer
"We know about Complex numbers, yet we do not have a numeric system capable of representing them (as single values)"
I think it is possible to represent complex numbers as single values: if we have z=x+iy than I can represent z as a 4-vector (y,x). Component y is time representative of the complex number and this component is alays orthogonal to the space comonent x in a Minkowski vectoriel space. In physcics component y can represent the energy of a corpuscle and component x represent its momentum. We can take it in other manner component y is the mean position of a corpuscle referred to a constant of measurement (or a meshing or a scale) and when this component is so great it tends to a constant i.e a new mathematics of numbers began.
Minkowski space is euclidian space (or flat space), we can generalize complex numbers to be repressented in a curved space and this will be totatlly new: what is the physical implications ? perhaps we can represent spin, electric charge, color...etc of a particle.
Charles St Pierre
"So, when does history end and math begin? Or is religion in the math, too? Then we have the math predicts religion
But: Only nothing real in the way of objects of worship? Surely, if everything is just math, then the existence and nature of God should be in the equations."
Math is based on thinking and writing logical equations, religion can't be in the math. Religion is based on faith "what is true". If God should be in the equations than it is not possible because God is infinite but equations are in our finite mind.
The question is what is science?
Physical science deals with everything measured in time, lenght and energy using math models. Religion is revelation from God and this revelation is another measuring system for our behaviour. I can say that religion is the continuous part of physics so it is SCIENCE in it general definition.
Lorraine Ford Numbers are categories. suppose we take some finite group, (to simplify,) and multiply its action by a scalar. Then the action described by the group will be different if the scalar divides the order of the group or some subgroup, than if it did not. So if we iterate the group, take sequential powers of the group, but also sequential powers of the scalar, modulo the order. Hmm. Action must be between distinguishable states. Else only one possibility.
Permutation group all points distinguished, thus well ordered matrix and operations. Yes, can permute rows and columns. A superposition of all possible actions. So... Permutation group symmetric under matrix operations. (Hypothesis?) All points distance one. But how does this project into a three space.? One dimension cannot change by itself.
One of the amazing things about the dictionary is that, in a sense, it spans the space of all possible knowledge. We can only define words in terms of other words, and all the words, certainly all the shared words, are in the dictionary conceptually speaking. the words all define each other. They're all defined by other words.
Unfortunately, lacking the inclusion of more primal sounds and concepts, it is rather dry.
Which brings me to Serle's Room.
cristi marcovici Suppose you had a millions years of memories, each moment as vivid as the moment you are in now. OK. Amaranth Lion. Got it.? Put yourself in the picture. You're the guy with a million years of memories, every moment as vivid as the one you are in now. Got it, Amaranth Lion?
Also, statistics are like that. You have to make (statistical) sense of things that are a lot more jaggedity than are shown in your textbooks.
Also, I think economists are taught that the economy is some sort of a (Money is Power?) perpetual motion machine in Econ 101. There's this picture in every one of them
Charles St Pierre
In the real physical world, symbols representing real-world numbers are obtained when people measure a category like mass or velocity, and write down a symbol representing the real-world number. These real physical world categories are things that only exist in relationship to other such categories. In the real physical world, numbers are not categories: categories are the things you measure to obtain a number.
However, there is an awful lot of fictional nonsense that goes on in people’s imaginations. And isn’t this a big problem these days? That people can't distinguish what is real and what isn’t real? E.g., people can’t even tell that there is a difference between mathematics and numbers which only exist in the imagination, and the real physical world "out there" with its lawful relationships and numbers which are represented mathematically.
Charles St Pierre
Fake news and alternative facts: at least one can say that they are interpretations of the real physical world, but still tethered to the real physical world. But the same can’t be said for mathematics and numbers: they are not tethered to the real physical world, and they exist nowhere but in the human imagination. The only real-world numbers that exist are the numbers that are obtained by measurement of the real physical world, where the real-world number is represented by a number symbol. Is it any wonder that fake news and alternative facts would proliferate in a world when STEM sets a very, very bad example, by being completely unable to distinguish between what exists in the real measurable physical world versus what only exists in the human imagination? Science/ STEM could be different if it started by admitting to a few facts about the real world.
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wild ideas should at least be discussed , interesting , a million year that's about the oldest arctic ice (that is currently under global warming influnce to melt down )
concerning power, i thought a little and i had the sketch of an idea maybe money should be like some kind of distributed interconnected ,with certain social behavior rules ,remote controls. such that persons can shut down / intrerrupt / pause/ verify to other person energy utilities supliers , a game to who consume less in various ways .
lets say living a million years is possible , zero waste with the most ecological footprint , there are other people and other risks increasingly dangerous that associated with any simple day to day activity , such that a person should do nothing in order for the million year to go over and just wait for the time to end . Charles St Pierre lets say it a cryo fridge with a camera in front that record everything , i have spent a large percent of my life in front of the screen , many hours a day, i could check my browser history vividly ,comparing it wont be that much of a different experience.
to an other extreme, let's say a single second is like a million years .
three points i want to ad not going to much beyond the scope of this situation, a) when a coincidence happen stop and listen as if time is frozen try to make other correlations, to learn or recapitulate b) if an object can be recycled a couple of times maybe the same can be done with memories more or less randomly . c) in the language i speak there is more or less conventional say/ expression present in spoken dialogues , that ties telling the truth with your own or other person mortality .
maybe the conversation between people can go in time width as opposed to in time length
Martin Rees , an space physicist, say that it will not be human that would reach other places like galaxies, quasars or further at the universe edges. i want to Knill all the people.
Rebeca
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KhakiHeron
I believe we can find a mechanism to represent complex values as single values - and I agree it likely is related to vectors. The example you give, however, remains with real values (x,y) and not a single value z - which could be thought of as the scalar value of the vector (which cannot end up as x+iy, as this is two real values and not a single complex value).
AquamarineJellyfish & CornflowerCicada
Whole numbers are abstractions - what is common to all single objects, what is common to all pairs of objects. Much of mathematics uses abstractions - what is common to all algebraic equations of the second order. Geometry can be more or less the same - what is common to all line segments, what is common to all squares, to all triangles. The geometry, arithmetic, and equations of math are statements about any object or concept that fits the abstraction. The equation of a pendulum is very similar to that of a vibrating string, or of a wave. The equation is about any abstraction of the concepts - which is why the pendulum equation can be applied to the pendulum, the vibrating string and a wave. Each physical system can be abstracted so that it fits the equation (maybe with some additional values or constants). The fact that the equations need to be tweaked to fit the reality is because no physical event exactly matches the abstraction.
The power of mathematics comes from this ability to abstract - and the equations can apply exactly to the abstracted situation. When applied to physical events, we can take an event and find that it is like the abstracted situation. As with the pendulum, string, and wave, we can find multiple events that abstract to the same (basic) equation. There are always differences between the physical event and the abstracted situation - always (we never get the exact values for every event that is represented by an equation). So mathematics is good at abstracted situations, it is only good to some degree of error when applied to a physical event.
Then there is the consideration of the symbols used for values, for the equations - for being able to communicate an abstract concept between people. This includes the numeric representational system (e.g., Roman numerals, ratios, positional real numbers, powers, logs), infinitesimal symbols (e.g., dx/dy, Newton's symbols, epsilon-delta), vectors, or matrices - and other mathematical symbols. These can vary significantly between societies, cultures, aliens - as they are devised creations not inherent to some deterministic appearance. Mathematics cannot progress without these symbols - and mathematics has been prevented from advancing without the introduction of new devised symbols. Our calculus would be more difficult using Newton's symbols than Leibniz'. We could not have the technology we have using just Roman numerals or just fractions.
Science and mathematics are very co-dependent, although there are few abstract situations (aside from simple arithmetic e.g., 1apple+1apple=2apples) that exactly always matches physical events. And the inexactness, or error terms, leave wiggle room for interpretation of which equations (or tweaks) fit the experimental results.
Science has a number of historic paths that have not taken us down the always 'correct' (in hindsight) path. So I do not see science as deterministic (nor do I see mathematics as such - for symbolic reasons).
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Lorraine Ford So- OK Here's the thing. IF we assume mathematics to be closed and separate from the real world, then we should have no concept of number whatever. And maybe that's true. Anyway, the properties of numbers are indelible in the roots of physics. You can't have an equation without them. Even if they're only approximate.
Thank you for your helpful discussion CornflowerCicada Country folk know its a lot more economically efficient to undersell ideas and things, rather than oversell them. A lot of these 'colors' seem to represent something more variegated than some mere "hue." JBTW.
“Whole numbers are abstractions”
But where do these abstractions exist? Whole numbers, rational and irrational numbers, mathematics, and all the associated symbols, only exist from the point of view of the human imagination. This is not to deny the “power of mathematics”, where mathematical symbols can be used to represent the real-world numbers and the real-world relationships that physics has obtained and deduced from experiments (despite some degree of error in the numbers).
Re the counting numbers: the number of planets in the solar system is not an actual real-world property (“what is common to”) of a collection of planets, a property that actually exists “out there” in the world. The number of planets in the solar system is something that only exists from the point of view of the human imagination. When analysed, counting is a many-step process, performed by people and some other living things, which also involves: 1) the ability of the counter to define the category being counted (e.g. first, define a planet); and 2) the ability of the counter to identify the category being counted (e.g. second, does a particular celestial object fit the agreed-upon definition? Is Pluto a planet?).
But, as opposed to what exists in the human imagination, there are numbers that actually exist in the real physical world “out there”. When particular categories of the real physical world are measured, e.g. relative position or mass, one gets a number, and this number is represented via the use of a number symbol. So real physical world numbers exist “out there” as opposed to the numbers that only exist in the human imagination.
“The power of mathematics comes from this ability to abstract”,
i.e. the power of mathematics comes from: 1) the human ability to invent and comprehend symbols; and 2) the human ability to represent the real physical world, and even imaginary concepts, with symbols. So, I guess that I agree with you about symbols.