Thanks Eckard,
You have added a third way of parsing the digital/money pair as regards to the actual counting. And I could offer a fourth in that digital reality costs money, although much less than before.
I agree that physical pursuits of the mathematical ideas of 0 and infinity have been (despite Aristotle) most important in building our modern world and its history, but I fear the unintended side-effects for my children.
Regards, John M.
Dear John M.,
You wrote "digital reality costs money, although much less than before." Perhaps you meant digital virtual reality and compared it with perceptually equivalent not yet digitalized alternatives.
I rather felt reminded of the cost for equipment like LHC that is designed as to search for a suspected digital structure of time and space. I see these efforts similar to the intention of medieval alchemists to make gold. Tschirnhaus and Boettger made white gold: china. Isn't the www a spin-off of Swiss physicists?
"Despite Aristotle"? Isn't his view "infinitum actu not datur" still correct? By the way, there were already ancient symbols for zero. Most likely ancient and medieval mathematicians hesitated using it because they understood the two the first number after what we are calling the neutral element of multiplication: the one. Not by chance, Leibniz invented the dual numbers and also the infinitesimals. I see an overlooked problem not in infinity and not even in zero but in a strictly ideal understanding of the basic measure one.
You complained: "I fear the unintended side-effects for my children." If I guess correctly, you do not like your children excessively consuming digital pleasures like gameboys, headphones, TV, internet, etc. Well, as I wrote: "Signal processing is superior if based on digital values." I even partially ascribe the present turmoil in Egypt and elsewhere to the desire for participating in such tempting pleasures. However such questions are off-topic. At least my essay deals with deeper issues.
Since I am retired, I do not fear side-effects that put my employment at risk when I frankly utter what is definitely highly unwelcome to many experts.
Regards, Eckard
Dear community,
While I am still waiting for responses by several contestants including Cristinel Stoica, I highly appreciate the private response to my essay I got from David Joyce. He is a professor of mathematics, an expert in history of mathematics. I will ask him again for his permission to put his reply on this public location.
In the meantime I would like to try and clarify to him and perhaps to you all which two old notion I would like to suggest for reinstating more precisely:
i) Euclid's notion of number as related to the ideal notion of unity
ii) a continuum every part of which has parts as still stated by Peirce.
Both old notions were accepted until the 19th century. While the notion unity is not identical with any object of consideration like length, area, a countable item, etc., it can nonetheless be attributed to it, and it shares its extension.
When the notion of number relates to the notion of unity, and a true continuum cannot be composed of any finite amount of extension-less points, which do not have parts, then there are no singular numbers. Brouwer's intuitionism comes close to it.
Accordingly, we should not declare Aristotle, Galilei, and Leibniz outdated and Peirce just an often drunk stupid American. Even if Peirce was an outsider, I consider him more intelligent than the whole folks including Dedekind, Cantor, Frege, ...
Let's judge the foundational consequences for physics. Shouldn't we consider numbers and continuum quasi orthogonal to each other?
Eckard
Hello dear Eckard,
All that is interesting.
You ask many things, I will do the same.....hihihi
How are your glands, eyes, brains,cells,...are spheres and spheroids?
Why our stars, planets, moons, BH also ...are spheres or spheroids if you prefer?
Why the rotation is so important?
What are our big revolutions,the wheel, the motor, the rotor, the turbins....?
How are our eggs, fruits,seeds,...?
A water drop, a wave,......Why the favorites sports of humans are with spheres?
How is our Universe for you? a square.
Why the particules have a big probability to be spheres?
a fly of birds........why the circles, the toti, the spheroids, the spheres and the rotations are so important and foundamental?
Why pi is so beautiful in its pure serie of infinity?
How are your hands? Why the man of de vinci has this circle ....I will say a sphere around?
How are really the space and the light thus in their pure BEC? The same simply, an pure entanglement of spheres and a finite serie.You shall understand why their rotations, spin.and orbt.are so important for a real polarity of evolution under specific codes of evolution between these 3 essentials inside the universal sphere......
Why the sphere, that is the question?
Why they rotate, why they are, why they evolve these mass?
Why the 3D is so essential....because the rotations need this foundamental.
Best Regards dear Eckard.
Why the maths show the road of the physicality? Because they can be finite also.....
a/0 Why ?
Why the real transcendance is relevant after all?
Steve
Dear Eckard,
I am flattered that you chose to respond to my posts. I will not try to parse the phrase 'deeper issues' since our premises and assumptions about our presence on earth may be very different. I would argue that digital reality and digital virtual reality are identical.
It is my understanding that divisibility produced nuclear power and weapons, and the human fascination for the infinite can associate with both cosmology and organized religion.
I hope you find this post less objectionable, otherwise, avocational.
Respectfully,
John M.
Please find attached what Prof. David Joyce of Clark University wrote to me.Attachment #1: Joyce.doc
The primes numbers are interestings....and Euclid said...n!+1.....them they are infinites in fact no? Perhaps if the university of Alexandria has some works about the numbers.....perhaps after all ,they proof what the 0 doesn't really exist ?
Tchebichev....n and 2n ....they are everywhere dear Eckard these primes.
1-1/3+1/5-1/7..........=0.77...
Between 0.740...and 0.78.....a beautiful symphony of sphere helps .....the arythmetic dear Eckard, the arythmetic ....pi/4 , the primes and the constan,ts,UNIVERSALS......it's a kind of road of distribution inside a sphere ....polyhedrization spherization.They make me crazzy you know these primes.
Zeta function....euler and poincarré fortunally have searched this conjecture.
Rieman more with complexs.
Why do you see those 0 on the 1/2 line of the graph.The Moebius function is interesting, isn't it AND ITS VALUES 1 AND -1.
The sphere dear Eckard, the sphere and its spherization shows the real distribution of numbers.The conjectures and identities are logic.
In fact it's a play with finites systems and infinities in their pure domais of distributivity and its sisters, the commutativity and the associativity.
A spherical distribution of numbers .......and the curves appear(see the0)!!!
Regards
Steve
Dear Sir,
Your essay is very interesting. However, regarding 0 and i, we have the following observation, because there is lot of confusion in this area. Here we present the mathematical view of physics.
Number is a property of substances by which we differentiate between similars. If there is no similar substance, then its number is one. If there are similar substances, then the number sequence begins depending upon the number of perception as one plus one plus one etc. Zero implies absence of the object of description at "here-now", even though it exists elsewhere. Thus, it is not a number in the normal sense. For this reason, no linear accumulation or reduction (addition or subtraction) is possible involving zero. Multiplication and division are non-linear accumulation and reduction. Since zero is not a number in the formal sense, non-linear reduction is not possible, because it is non-existent at here-now. Multiplication with zero takes the object to the realm of non-existence, thus reducing it to zero.
Regarding i, the concept itself does not stand mathematical scrutiny, as it fails the test of logical consistency, which is the benchmark for judging the validity of a physical statement. Not only it is not a number (because it is un-physical), but also the squaring of complex conjugates is un-mathematical. This is the reason why complex numbers are not considered in programming. In any multiplication, we multiply not only the numbers, but also the signs. This is because the signs represent "ownership". If A has 10 apples, he owns it. If he has -10 apples, he owes ten apples to someone else. This simple, but fundamental mathematical principle is overlooked in squaring the conjugates. Thus, the whole mathematics of the "wave-function" is un-mathematical.
We have discussed on this and related subjects elsewhere. Kindly read our essay for further details.
With kind regards,
basudeba
Dear John M.,
What about my use of the metaphor "deeper" I was not consequent. In principle, I consider reality as the basis of all. In that I differ from those who believe that the world has been build according to given laws from at least one primordial element. While I do not exclude this possibility, I am reluctant to swallow any belief in genesis without at least imaginable evidence or applicability.
I am using "deeper" synonymous with a "higher" level of abstraction and generalization.
However different our premises might be, I hope we will be in position to negotiate and arrive at sometimes unexpected agreements. So far I did not yet understand in what sense you equate digital reality and digital virtual reality. Isn't the term virtual reality unmistakable? I feel tempted to conclude that in your understanding digital reality does not refer to the idea that time and space are digital at the most elementary level.
According to my dictionary "objectionable" means offensive and unacceptable. Be sure I do not feel any utterance of you objectionable. On the contrary, I feel happy if someone stimulates me to rethink my own view. Admittedly I did not understand how "the human fascination for the infinite can associate with both cosmology and organized religion".
Regards, Eckard
His words are interestings.The continuity and the discreteness in a real distribution, harmonious.The sphere helps of course.
This Euclid was a sacred searcher in all case.The prof David Joyce seems well knowing this matter and these numbers.Interesting his point of vue about the o, the - ...
Regards
Steve
Steve,
Educated experts know that Alexandria was the capital of Ptolemaic dynasty from 323 to 30 BC. The Ptolemaic system is however named after Ptolemaios Claudius who also worked in Alexandria but from after 83 AD to 161, i.e. much later. You should meanwhile be familiar with him because I already told you he anticipated your spheres.
Euclid lived from 365 to about 300 and worked at the Museion of Alexandria, which was the ancient university. Unfortunately, the belonging famous library with 600,000 handwritten books burned down in 48 BC.
I will check your hint to Moebius.
Eckard
Fortunalmly I am the first for the real unfication of spheres....
I repeat for our scientists friends from over the world.
QUANTUM SPHERES(and their numbers and volumes and rotations!!!).....COSMOLOGICAL SPHERES(this number is fascinating and probably the same for the uniqueness!!!).....UNIVERSAL SPHERE(and this sphere evolves!!!)
the real toe, the real gut the real unification and you know it like all here, I say that humbly of course, I am not better than others, just I show my discovery and I discuss ....in fact it's logic all these proportionalities with rotating spheres, it's logic that the universe is a sphere in improvement and optimization.It's logic also that the link between the small and the big is these spinning spheres.......it's logic all that simply and it's foundamental.We have so many works to do still for the discovery of this sphere and its central sphere where all turns around, it's logic and rational I repeat humbly.We live indeed on a sphere , we turn around a sphere, we are composed by spheres, we we turn around an center, we turn inside this universal spheres, all turns, in us, around us, ....all dar Eckard is in this universal and spherical logic.Ptolemée probably like many others thinkers from the past shall agree with my general conclusion.And they shall help me I beleive in this research of truths and truth.The complemenatrity as said Borh is so essential when the foundamentals are respected.
Regards
Spherically yours
Steve
Dear Eckard,
You are correct. My understanding is exactly that time and space are not digital at the most elementary level, even though digital representations most accurately describe the current phenomenology that we have observed. So to use hearing as the analogy, a digital recording represents the original with less signal to noise issues than analog recording, as long as the sampling rate is fast. You are undoubtedly an expert in this area, so I prefer not to look more of a fool. Generalizing, an event can at best be represented after the fact, but never repeated at exactly the same time (unless the second law 'is not even wrong'). And so the issue is not about what is the reality but rather how it is represented after the fact. This was the point of my essay, and this is why I sarcastically suggested that infinitely many universes could occupy the same space. Continuing the analogy(!!), digital data could play multiple recordings virtually simultaneously on discrete systems - this a little joke.
Regards, John M.
Dear Basudeba,
Edwin Klingman's comment on your essay made me curious. I asked you to comment on mine. While I would appreciate you even more taking directly issue concerning my definitely hurting conclusions, you addressed a perhaps important issue.
Unfortunately I have to admit a lot of disagreement, for instance if you declares zero unphysical and THEREFORE no number. Aren't numbers in general unphysical?
Ancient mathematicians considered the two the first number. In medieval Europa the line of positive and negative numbers including zero was introduced. I see this paving the way for superior calculus while simultaneously creating a risk of misinterpretation.
Does the concept of i really not stand mathematical scrutiny?
Are multiplication and division really non-linear operations?
Regards,
Eckard
Dear John M.,
I consider my Fig. 1 an important part of what I have to tell: The non-linear cosine transformation changes discrete into continuous and vice versa. The inner ear works similar. Accordingly, it is difficult to decide which presentation immediately corresponds to reality. I consider ideal continuity as unrealistic as ideal discreteness. Nonetheless I share your view. Time and length seem to be more natural as compared with frequency and wave number. Perhaps Peirce was correct in that temporal and spatial distance are not lattices.
Regards, Eckard
Eckard
Some brilliant stuff again, as I've grown to expect.
We're up against some good competition, but what stands out mostly for me is how much science is still 'belief' led, and beliefs really do depend on what paper we read.
I was posting something for Jason in the blogs this morning, and thinking of you, I went deeper into the archives and found the rich seam I was after, in fact one I hadn't seen before from as far back as 2002!
http://cerncourier.com/cws/article/cern/28606
I won't swamp you with others, just to say things have moved on much since then, but still missing the key, the solution to it all now provided by the DFM. I'm still trying to get it published, but I suppose the attached and my essay here, prove that even if it does get published it probably won't be understood and will make no difference.
I'd be delighted in your views on the above and my essay if you can find time to read them.
Very best wishes
Peter
Please find attached my preliminary reply to Prof. David Joyce.Attachment #1: Joyce1.doc
Dear Steve,
Thank you for making me aware of Moebius function. Usually I do not like playing around with numbers like a game. Such pure mathematics reminds me of pure speculations by Stiefel, the fried of Luther. Sometimes they are of relevance, e.g. concerning symmetries of crystals or within atoms. Ray Munroe (while he promised to read my essay he seems to lack counterarguments) and others here seem to be experts in this field. Gauss, Moebius and contemporaries found out a lot of peculiarities in so called theory of numbers. Therefore they abandoned the traditional link between the notion number as a measure.
In principle, there is nothing wrong with negative and imaginary numbers except for being prone to wrong interpretation due to an arbitrarily stripped off link to an original reference zero. As the title of my essay indicates, the usually introduced once or twice redundant ambiguity tends to be even excitingly superior. Engineers like me benefit a lot from so called linearized small-signal consideration, i.e. restriction to symmetric small enough alternative components.
However, I am not aware of a single case where real processes could not be described, in principle, without the arbitrarily attributed negative and complex numbers.
Temporal as well as spatial distance (unilateral time, and radius of a sphere, respectively) are originally not subject to symmetry. That's why I suspect SUSY ill-founded if understood as real. Do we really need complex calculus as to describe the mirror symmetry of bosons and the antisymmetry of fermions? See my admittedly naive hint to a quite simple trigonometric relation.
Regards,
Eckard
Dear Peter,
Having tried to read your essay twice, I must confess being unable to clearly understand it. On the other hand, you seem to claim some sort of scientific breakthrough. For that reason I asked other contestants for their opinion with no avail. There is only one piece of advice I possibly can offer to you: Please omit any unnecessary detail from your argumentation, avoid unusual or even unknown abbreviations, anticipate distrust, and provide compelling arguments.
At the moment I do not read blog-related postings. Thank you for the link.
Best wishes,
Eckard