"The Mathematics we use ... still to send toys to Mars or Land on the Moon ... is based on the four basic Operations: +,-,* and /. Until here we are using simple tools to do complex Jobs."

Is it good or bad? (I couldn't get it from your comment.) I think it is good when we use as simple tools as possible to solve the task at hand. Complexity costs more, and every complexity is just...

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"The Mathematics we use ... still to send toys to Mars or Land on the Moon ... is based on the four basic Operations: +,-,* and /. Until here we are using simple tools to do complex Jobs."

Is it good or bad? (I couldn't get it from your comment.) I think it is good when we use as simple tools as possible to solve the task at hand. Complexity costs more, and every complexity is just multitude of simplicities.

The basic arithmetical operations you mentioned are actually all we need, if you understand them correctly: as geometric operations. For example, multiplication is repeated addition, but not only that – it can be seen in a more general context as a proportion which can be expressed geometrically as geometric similarity of figures, the purpose of which is conversion of units between those similar figures (see Section 2.2 and Fig.3 in my essay). This way it could be easily (and correctly) extended to higher dimensions of geometrical numbers (such as quaternions, octonions etc.). Scalar and vector products are not correct generalizations because they're not multiplication, they don't fulfill its axioms.

Two of the arithmetical operations you mentioned – addition and multiplication – are actually encoded in the very definition of number (if we define it correctly, that is, not with nested sets but with functional operators). Addition comes from the fact that each number is a vector which stores information about how to go from the origin state (0 by default) to the particular state. If the origin state is not 0, but some other number, you get addition.

Multiplication comes from another property of number: that it is a multiple of a unit. By default, this unit is 1 (the "standard" unit), but you can replace it with some other number, and the number will then repeat this number instead, which is multiplication.

The other two operations you mentioned (subtraction and division) are just inverses of the former two (I like to think of them as "magic counter-spells"). Subtraction comes from complementing addition to 0, and division comes from complementing multiplication with the unit (1). This complementing is what Algebra is all about (the modern definition of algebra as just a tuple of operators and their operands lacks this important detail about balance). Division is then repeated subtraction similarly to multiplication being repeated addition.

Also, you forgot raising to powers, taking roots, and logarithms, which are the next level of compression of arithmetics (powers are repeated multiplication, roots are fractional powers, and logarithms are repeated division and arithmetic-geometric proportions).

All these arithmetic operations make a hierarchical structure, they are simply levels of compression in our mathematical notation, but they can be all boiled down to adding up units (pebbles).

The more "advanced" parts of mathematics, such as calculus, differential equations, divisibility rules etc., even geometry, can also be reduced to arithmetics, if understood correctly, because arithmetics is geometrical in its nature. But the emphasis is: if understood correctly. We don't really need new math (as of yet), we rather need to stop and review the mathematics we have, because from what I observe, there is a lot of misunderstanding in it, especially in the basics (and when the bases are unstable, the entire building is shaking, and it can rumble one day).

Sometimes the corrections required are subtle (but important!), as with the definition of power: it is not, as Wikipedia and the textbooks say, multiplication of a number with itself. This definition is wrong. The correct definition of power is: multiplication by the base repeated as many times as the exponent tells us. The difference is subtle but important, because the incorrect definition stops us from seeing why is a^0 = 1, for each a (we don't really need an exception for 0^0 if we understand correctly what it means and how it works geometrically).

But sometimes a more serious correction is required, as it is with calculus. We are told that we need to use infinitesimals and limits, but this leads to many paradoxes and confusion, and is not really needed. When one understands differentiation correctly, one can do calculus with simple finite numbers and ratios, because calculus has nothing to do with infinitesimals – it is rather about ratios and proportions between functions and their values (see Section 4 of my essay). It also comes naturally from the definition of number as vector, because vectors are formulas for change, and changes are described by relative differences (which are differentials, if we are interested only in linear approximations to these differences, or tangents).

Also, the multi-variable (or vector) calculus comes naturally from this fact: it's just calculus on vectors in more dimensions than 1. And the inherent properties of vectors (magnitude and direction) maps directly into the two vector field differentials we know: divergence (stretching of the magnitude) and curl (rotating the direction). We need both for full description of the field (see Section 5 of my essay).

As to the time and how we measure it: notice that we always measure it with motions. If nothing moves, we cannot tell the time passed. But time is actually a measure of distance. If you're surprised by this fact, read my other comment in this thread, and take a look at Section 3.3 of my essay, where I explained it in more detail. It's not good to blame Einstein, since he was perhaps the only person on Earth since the Ancient Greeks who made any progress in understanding time: he noticed that time is inherently connected with space through motion, so if motion is relative, then our measurements of time and space will be relative too. The only detail he missed was the one I describe in my essay: that time is not a separate dimension, but it is already among the spatial dimensions we know. But you're right that a thorough understanding of what that little `t` means in our equations is probably the most important aspect in Physics, because this `t` appears in nearly every physical formula. Incorrect understanding of what it means leads to confusion we have now: confusing time with our psycho-cognitive perception of time, or confusing time with memory of the system, or making a separate dimension of time, which leads to incorrect interpretations of Minkowski's spacetime diagrams, which in turn leads to such absurds like "exceeding the speed of light will cause the time to flow backwards" or "breaking causality" (those are statements made by the most famous physicists! I can make proper quotes if needed).

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"While I guess, you are not a professional"

You don't need to guess: I stated that explicitly in my bio, because I knew that someone will play this card sooner or later. I haven't followed any formal academic career, I don't have a PhD, this is true. But this doesn't automatically mean I'm stupid or incapable of doing Math or Physics. On the contrary: I spent my all idle time for digging...

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"While I guess, you are not a professional"

You don't need to guess: I stated that explicitly in my bio, because I knew that someone will play this card sooner or later. I haven't followed any formal academic career, I don't have a PhD, this is true. But this doesn't automatically mean I'm stupid or incapable of doing Math or Physics. On the contrary: I spent my all idle time for digging through books, papers, and on polishing my own ideas when I see there's something wrong with the ones I encounter. This brings us to the next quote:

"you are claiming to understand mathematics correctly"

Yes, but I'm not claiming I'm omniscient or infallible, or that correcting some misconceptions of Mathematics makes me better from others. We're all humans, we can make mistakes, there's nothing wrong with it, but it is better to review the collected knowledge from time to time and correct the errors of the past than complaining that someone is trying to do that. I appreciate how scientists of today are devoted to answering the advanced questions. But there are still some unanswered questions left behind in the more basic stuff, which no one seems to investigate anymore, considering them "too simple to bother with". But I repeat: one cannot build a skyscraper on a swamp. If the bases are unstable, the whole building will shake. Dealing with the advanced stuff before making the basic stuff straight first might be dangerous and pointless, since wrong assumptions can lead to wrong conclusions.

I claim what I claim as a result of many years of investigating these basic stuffs. As with any claim, it is not the claim which is important, but its verification (that is, how much it fits the truth/reality). And if you see anything wrong with my claims, feel free to debunk them. I can make mistakes as well.

"I doubt that you will for instance grasp why I object to "adding up units (pebbles)""

Try me. Unless it is you who thinks of yourself as someone better than me, or of me as being incapable of grasping your vast knowledge. Don't get me wrong, but your tone is very patronizing and scolding, which doesn't seem much professional.

As to the "pebbles", I admit this was an unfortunate shortcut of mind, which I though anyone with enough mathematical background will understand. But if you prefer being picky, then let me explain it a bit further: What I meant to say is that every number is some multiple of a unit, and without defining the unit, one cannot measure anything – every other numbers are undefined in that case. What I didn't meant (and you seem to suppose about me) is that there are only natural numbers or that everything can be reduced to them. In a way, this is true, since we describe non-natural numbers in terms of natural numbers (e.g. rational numbers as ratios of two natural numbers; irrational algebraic numbers as radicals of natural numbers or their ratios, etc.). But I'm not saying that natural numbers are all that there is. I'm fully aware about rational, irrational, algebraic, transcendental, imaginary, complex, etc. But if you read my essay, you'll see that there is also a lot of misunderstanding about these numbers and how are they constructed. If you object my approach, you should object the set-theoretical approach even more, since it boils down to natural numbers and countability of sets, and lacks any notion of magnitude, not to mention direction of numbers. Unfortunately, I don't see much people questioning these basic axioms of modern Mathematics. I see this as an example of how the formal education can shape our thinking in a way that we could be incapable of questioning what the authorities have told us. If it happens that you belong to that group of people who can listen only to what the PhDs are telling them, and consider everything which comes from a non-scholar as false "by definition", then I am sorry, I cannot help you.

"and why I consider the essay of Thomas Phipps a key to the insight that length contraction, Poincaré's spacetime, and all that have been unfounded."

I haven't read Mr. Phipp's paper yet (but surely will when I find some time), but contrary to your strawman argument, I agree (in a way) with what you said about these notions from Relativity. It again boils down to proper understanding. Relativity is not "all wrong", since the formulas are correct, the predictions are correct, confirmed experimentally in labs and in every CRT TV. The problem is with the interpretations of these formulas and experiments, and the incorrect conclusions people draw from these, about the nature of time, space, motion, relativity, consciousness etc. (which does not surprise me, since there's a lot of confusion about time and space already). It is not the "length" which contracts, but matter waves we use to measure lengths. Similarly, it is not "time" which dilates, but our perception of it, which depends on our point of view and relative motion. It is not that the speed of light is "constant with respect to everything", but it is that everything which stretches and contracts to make an illusion of constant speed of light for any observer, which is himself made of matter waves, and these waves follow the Doppler effect too. One cannot observe its own Doppler effects, therefore these effects cannot be detected in "relative rest". Physicists seem to forget that the Michelson interferometer is not some abstract geometrical device, but it is made of matter, which in turn is made of waves, as the light is too, and they both fulfill the same Doppler effect, so their Doppler effects cancel, resulting in no shift in the interference fringes. The problem with Relativity is that we try measuring light and matter with themselves, which makes an illusion which we call Special Relativity, and every single laboratory instrument will confirm us in this illusion. We can escape this illusion only with our minds, by reviewing the axioms.

As to the spacetime, I agree, there's no such thing, because time is not a separate dimension (not in the same way spatial dimensions are) – it is already contained amongst the spatial dimensions, as a measure of the distance traveled by a reference object in motion, which we call "clock". Minkowski's spacetime diagrams are a useful tool for analysis, but we should not see it as anything more "real" than a graph of temperature versus pressure, for example. Temperature and pressure are dimensions too (since they can be measured), but not at the same rights as spatial dimensions, so don't get misled by the fact we use spatial dimensions of the graph to describe them – this is just a geometrical ploy, a mapping which allows us to "see" them and "analyze". Similarly, Minkowski's spacetime diagrams are just for "visualizing" and "analyzing" events, it is not a diagram of reality and it shouldn't be confused with it. I often see well-known scientists saying that when something moves faster than light, it goes "back in time". This is an example of not only confusing the graph with reality, but also of misinterpreting the graph altogether – for something to move "back in time", it has to cross the horizontal axis of the diagram, that is, move with a speed more than infinite (and this would really be absurd). But there's plenty of room between the light cone and the horizontal axis of space. There's no "time reversal" in this area yet. It just extends the range of our consciousness: we can know about the event which occurred before we see the light coming from that event. For someone who can only see the light or other electromagnetic phenomena, this might SEEM as seeing the future, but this is only about how fast one can get some information about the distant event.

"If you are really willing and able to reveal a fundamental mistake, please explain what worried the late Einstein: the now."

Nope, I'm not here to point mistakes, I'm here to present the alternatives which I consider correct. I'm not here to dance to your music either, or starring the strawman you're trying to project upon me. I'd just say that playing the strawman argument, as well as moving the burden of proof to someone else, are considered logical fallacies. Patronizing tone and arguments ad persona (e.g. pointing out my lack of "professional" career) also doesn't help your case. Truth is truth no matter if it came from the mouth of a wise, a fool, or from the beak of a parrot.

"It seems to me, you share his denial of the border between past and future."

Where did you get that from? I nowhere said that.

But before we get into this argument, let's make sure we're speaking about the same things and agree upon the definitions. There's a distinction between what actually happened and our knowledge that it happened. People often use the name "past" to both of them, despite they're two different things. Relativity is all about distribution of information with different media (mostly light), therefore in SR there could be disagreements among the observers about what happened when, and which events belong to their "past".

Once I invented a simple story which explains this:

Imagine you have a friend who is blind. He can know about things only by hearing the noises they make. There's a storm coming, and you've just saw a lightning somewhere far away. The light from it has already arrived to your eyes, but the sound is still approaching. So you tell to your blind friend: "Pay attention, you'll hear a rumble in 3 seconds", and after the 3 seconds, your "prophecy about the future" fulfills, to the amazement of your friend who now thinks you're a psychic, because you "predicted the future". The thing is, this was "future" only to him, because it was outside of his "sound cone", but it was inside of your "light cone", so it is already in the "past" to you. The reality is that the lightning stroke already, for both of you, so it is already in the past. It's just that the difference in the speeds of the signals you use to get that information makes a distinction what is perceived as "past" and "future" by you and your friend.

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Whose fault is it that there's not so many essays written by women? Is someone stopping women from submitting their papers? In the European Union, there are movements to enforce equality between men and women by law. These laws would require 50% of the available chairs to be chaired by women in governments, boards of directors in companies etc. They think this will introduce more equality...

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Whose fault is it that there's not so many essays written by women? Is someone stopping women from submitting their papers? In the European Union, there are movements to enforce equality between men and women by law. These laws would require 50% of the available chairs to be chaired by women in governments, boards of directors in companies etc. They think this will introduce more equality between men and women, but in reality, this will only cause disaster, because they will hire women only to fill the 50% requirement instead of basing on their competences or skills. There's nothing which stops women from applying for these chairs at present, but from some reason, they don't apply or don't qualify, so enforcing equality not only won't help, but it will also make it worse.

As to the essays: This is contest is about science, not fighting for women's rights. If I read your essay, I don't care if you're man or woman; the only thing I care is relevancy, originality, or in short "how good it is". If it is not good, the fact that you're a woman or not, won't change anything, so blaming it to women suppression is a cheap excuse.

(Just to be clear: I haven't read your paper yet, so this is only a figure of speech, not a judgment about your paper.)

Re closed systems: Our entire Universe could be seen as a closed system. True, the Mandelbrot's set is a closed system too. But if you start digging into its details, you will see that this closed system is actually infinite in detail and amazingly beautiful, even if it is bounded in a finite region of space. the same applies to our Universe: it is bounded, and its laws could be set and limited, but still they can be combined in an infinite number of ways to produce unbounded complexity and beauty. That's how Nature solves this finite/infinite conundrum. See the last section of my paper for more about that.

Re: robotic male-views which destroy our planet: In a way, I agree. But it is not only men who represent these views. But I'd ask you: what kind of women's views you propose instead? And why do you think such views are reserved just for women? Couldn't there be men who love nature, beauty, symmetry, art etc.? Now that's stereotypical thinking!

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Lorraine,

I now feel that I have been horribly misrepresented.I certainly don't think what Jonathan or anyone else is doing was pre-specified at the beginning of time. You will see in my essay discussion page -reply to Peter- that I consider hard determinism 'absolutely' abhorrent, incorrect and in need of overthrowing as the accepted wisdom.In that reply I spelled out the great...

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Lorraine,

I now feel that I have been horribly misrepresented.I certainly don't think what Jonathan or anyone else is doing was pre-specified at the beginning of time. You will see in my essay discussion page -reply to Peter- that I consider hard determinism 'absolutely' abhorrent, incorrect and in need of overthrowing as the accepted wisdom.In that reply I spelled out the great importance of identifying the category error leading to the grandfather paradox, as it was not discussed in the essay.The essay being 'matter of fact' without discussion of underlying philosophical issues and issues of morality.

I have, in this thread, explained my view of the open and closed universe question. The Object universe is only one configuration that is undergoing change to become the next singular configuration. It is dynamic, ever changing, the previous configuration being the input to the next in a sequence. There is no material input or output from the universe and in that sense it is closed. However in the sense of being creative it is open because the old is recycled into the new not fixed in time, and there is no concrete future. So unlike the space-time continuum in those respects. I have also explained that the visible universe, the image output of sensory data processing, is open in the sense that new potential sensory data is being received changing the image. With the structure of reality I have illustrated participation in the creative process is possible, within the material Object reality realm, precisely because it is not pre-ordained, pre formed waiting to be discovered.

Re-iteration can be seen in the natural world in the ripples in the sand at the sea shore and the erosion of sedimentary rocks revealing their strata as well as fractal dimensions in coast lines and river flows. The mathematics is in nature but may be extracted, 'distilled' out, into its 'unnatural' pure form by the human mind. As has happened with the Mandelbrot set. Neither pre-existing discovery in a platonic realm in pure form and not created entirely by mind alone.In my discussion with Peter Punin I used the analogy of the properties of pure alcohols distilled from nature. We can know their properties without those coming from a perfect realm of pure chemicals or being invented by the mind alone. Nature already has first claim on re-iterative processes. My essay starts The golden ratio and growth, fractal geometry and natural scale invariance: such beautiful correspondence of mathematics and natural forms.....

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James, you're right. There are very bad people amongst the contestants, who seem to manipulate the scores by granting the lowest score as soon as someone they don't like raises above 5.0 limit. My and my friends have observed many examples of such activity. One example I present in a comment on my essay's thread here.

I even have a proof that these people are fully aware of what they're...

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James, you're right. There are very bad people amongst the contestants, who seem to manipulate the scores by granting the lowest score as soon as someone they don't like raises above 5.0 limit. My and my friends have observed many examples of such activity. One example I present in a comment on my essay's thread here.

I even have a proof that these people are fully aware of what they're doing and do that purposely, as a form of... I don't know... punishment? banishing? to those people they don't agree with. Namely, when I (politely) asked Mr. Sylvain Poirier to review my essay, he replied with a very rude way, calling me "crackpot", "obscurantist" and what not, and paying me justice by rating my essay with the lowest possible score: "1". He admitted he did it on purpose. Quote:

"With your insistence to put forward your nonsense, you are really making me willing to give you rate 1."

And so he did, which lowered my score from 4.9 to 4.5.

I cannot understand such behavior, I was not insisting on anything, I politely asked for review, not even for giving me any score, and I asked only once.

His other "kind words" clearly show what kind of person he really is and what does the "love for science" mean to him. Quoting again:

"You are just a crank like others, what I call "obscurantists"."

Not very professional way of reviewing, ain't it?

"You stand with the crowd of ignorants who have no clue about science and pretend to refute it, and dominate this contest by their large numbers. They believe that they are a persecuted minority, now they are happy to find themselves in large number in this contest, and they imagine that it will make them win against the elite of scientists who commit the crime of dominating the world by their higher intelligent that the people decided to dismiss as fake. Just like a Marxist revolution, they believe they will create heaven on Earth by massively standing up and killing the minority intellectuals which they accuse of all their miseries. I stand for science (yes, the Copenhagenists and such)."

(Seems like this guy has some serious mental problems, and when he encounters anything he disagree with, he releases a whole lot of aggression and unfounded accusations. I can also see some signs of paranoia.)

"There is no problem about division by zero. There are only idiots who make problems of from this joke by inventing the need of dividing by zero where it does not make sense and they are making up the idea that it should make sense and that we can get an amazing problem to solve by senselessly throwing signs on a paper and insisting it should surely mean something wonderful just because it is senseless, so that it is surely wonderful to wonder what a senseless pack of random symbols absurdly aligned on a piece of paper, like a painting done by the tail of a donkey, should really mean. You can get the same thrill by studying the sentence "This sentence is false", if such nonsense is what you are fond of."

(Typical strawman argument, he tried to impute me something which he could then object to.)

"It seems you are inventing problems which do not exist, only because of your own failure to understand what is already clearly understood."

Sorry I do not think this is serious.

(A remark regarding my statement that differential calculus does not require infinitesimals and limits, since I show in my essay how it can be done with just finite numbers and their ratios, using simple geometry and basic algebra.)

Seeing your essay, it appears that you do not know quantum physics. I think there is not much one can have to say about fundamental questions in these conditions.

(Well, he surely knows me better than I do, then, despite he has never met me and he couldn't have any ways to find how much do I know about quantum physics I supposedly know nothing about. But oh well, being judgmental doesn't need proofs.)

I guess that telling about that to the organizers won't change anything (I already did it and nothing has changed under the sun), so I wrote this comment only to make it clear to other contestants who hold to their values and don't use their scores to diss other people.

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