Comments

  • The Decay of Science
    ... regain our innocencetheRiddler

    It appears you've never lost yours. Congratulations.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    The only way your work will get a fair hearing is to assemble several academics in several disciplines as a group and have them analyze it together. This might be possible if you have the money. If you don't have the money you could try GoFundMe. I doubt that would work, however. Better to find an old rich patron and convince them to support an investigation.
  • The Conflict Between the Academic and Non-Academic Worlds
    Similarly, becoming an academic or a person with an advanced degree is too easy these days.baker

    Really? Just your opinion?
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    I was a little concerned about , since the number of math symbols might be countably infinite, but finite strings of those symbols are countably infinite, so your summation makes sense. However, if one assumes the number of possible math symbols is uncountable (?) it's a different matter.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    How about topology or a similar discipline, where we may not be talking numbers at all? Functions of a non-measurable set? A function of a set whose existence is suspect? Intricacies like this. Subject to your experimental ideas? Places where math becomes more philosophical than numerical? Paradoxes?

    I'm just saying it's easy to write down the definition of "facts", but rounding them up is another matter. You are trying do encapsulate or describe all of mathematics in a few lines, when no one knows what "all" of mathematics is.
  • The Conflict Between the Academic and Non-Academic Worlds
    What concerns me deeply is our attitude towards our knowledge base, and how we're limiting exploration and imaginationtheRiddler

    Let's see, about 140 articles on mathematics research sent to ArXiv.org daily. The lack of imagination is astounding.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    So please, by all means take a crack at itAlexandre Harvey-Tremblay

    Another Link

    I'm not arguing since I know very little about the subject. Do your atomic facts include non-computable functions? Just asking.

    But I'm curious about Wikipedia, as I have one of the many, many articles there. I'm sure the number is finite, however!
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    The world of mathematics is exactly equal to the domain of a universal Turing machine.Alexandre Harvey-Tremblay

    Depends
  • Strange Concepts that Cannot be Understood: I e. Mind
    Light speed being invariant under motion. Quantum effects. Etc.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    Since halting programs are arbitrarily complex and subject the incompleteness theorems, modern notions relating to mathematical undecidability are leveraged to create a 'trial and error' foundation to their discovery, such that one is required to run programs to completion ---essentially to perform 'mathematical experiments'--- to discover them, thereby permitting a re-formulation of mathematics conductive to experimental methodsAlexandre Harvey-Tremblay

    As an old mathematician I can't imagine putting some of modern abstract math into the context of Turing machines that halt, which they may or may not. The world of mathematics is so enormous now no one knows how many subtle varieties of research projects are in play. Can you find out how many math pages are currently on Wikipedia? I am curious.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    I admire your efforts and your tenacity. If I were younger I might look into the math you use, but at least superficially it does not look seriously flawed. KB seems uncountable, and yet you sum the f's over it for Z. There are ways of doing this of course, but the concept is usually non-productive. Maybe KB is countable.

    But it's all beyond my specialties. The philosophical aspects are for others to assess as well. It all looks very vague and a little suspicious. You need to get verification by mathematical physicists. That would add credibility. Good luck. I admire anyone who digs into sophisticated math as you have.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    However, the knowledge base formulation can derive the laws of physics indubitably in a few lines, whereas the formal axiomatic system representation is plagued with axiomatic gaming and other problems.Alexandre Harvey-Tremblay

    Show how F=ma comes about in a few lines through your system.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    Maximizing the degree of disorder in a knowledge base is like scrambling intellectual eggs.

    Good nite. Talk tomorrow perhaps.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    A knowledge base in math seems incredibly vague unless one demonstrates actual theory within it. A collection of programs says no more than a collection of theorems - neither illuminating the vastness of the subject. There's not even a consensus among mathematicians on the number of specialized areas of mathematical study. The immensity of material and thought makes "knowledge base" meaningless, IMO.
  • Is there a unit of complexity in mathematics?
    You've gone down the path of algorithmic theory again, which has little to do with a typical mathematical proof. Not my bailiwick.
  • Is there a unit of complexity in mathematics?
    It sort of strikes me as odd that the only physical units to determine complexity in mathematical computations would be quantum computers with qubits... What do you think?Shawn

    New to me. Provide a link or two.
  • The theory of everything; formulated so as to be indubitable and thus forming a final theory
    1+1=2 and the program terminates, because it is programmed to do so. So this is a piece of "mathematical knowledge" or "fact". You state that to learn what math Bob knows one should not resort to axiomatic systems but to "mathematical knowledge", which would not be subject to axiom gaming. It might seem you are saying, take the math that has accumulated over the past two millennia before the modern attempts at axiomatizing the subject and consider these as mathematical facts. The fundamental theorem of calculus thus becomes a "fact" and modern set theory and foundations are irrelevant.

    Or, are you talking about the theory of mathematical proofs as a computer topic? The idea that any math
    proof is in essence a string of symbols.

    Guess I don't know what you are talking about. :roll:
  • Is there a unit of complexity in mathematics?
    A mathematician might say, "That proof was quite complex". Another might add, "Yes, but elementary!"
    Both could be correct.

    Complexity of proof is a kind of meta-mathematics idea that most mathematicians wouldn't be interested in pursuing. More likely a computer scientist of some sort.

    Beyond that, there is complexity of mathematical specialties. Euclidean geometry would be considered fairly light on complexity as compared with Scheme Mathematics
  • The Conflict Between the Academic and Non-Academic Worlds
    That question is floating in the air for me. Why do you ask it?Tom Storm

    If there is conflict between academia and the non-academic world, there is assuredly meritocracy in the former within disciplines, leading to personality if not funding squabbles. Sometimes those involved might assuage their feelings by displaying a touch of arrogance towards the less educated. This is unfortunate, but occurs occasionally. It's not pretty. On the other hand, higher education itself does not lead to meritocracy in a more general population since standards vary significantly across the globe. Just a few random thoughts.
  • The Conflict Between the Academic and Non-Academic Worlds
    In 1951 they didn't need to ask themselves, "Will x news headline cause anxiety and depression?" because maybe only thirty percent of people in the neighbourhood even read the newspaper on a daily basis.kudos

    Long before that defense pundits and military planners carefully manipulated news media to support the war effort. And perhaps not everyone read a newspaper, but almost all listened to the radio.
  • The Conflict Between the Academic and Non-Academic Worlds
    In a larger sense, is a meritocracy unfair?
  • Socialism or families?
    ↪Athena
    Well then somebody ought to hurry up and tell the Scandanavian / Nordic countries that they've been doing their brand of welfare-state capitalism wrong for almost a century.
    180 Proof

    Is There a State Crises in Sweden?

    Food for thought. Balancing a welcome carpet for immigrants with social welfare movements. Law and order issues. And more. Sweden's wealth distribution figures are similar to those of the US.
  • The Conflict Between the Academic and Non-Academic Worlds
    If you attempted to apply the idealized structure of mathematics to physics problems you’d encounter unexpected results because the real world doesn’t always deal in easily determined discrete quantitieskudos

    In a sense calculus has an "idealized" structure and physics cannot do without it, but you must be referring to set theory and foundations, and the axiom of choice, and the physics I am barely acquainted with does not require the latter.

    The academic may know a lot, but they don't know how to truly behave like a layman. They can never know how to not know what they know, and that is a weaknesskudos

    This sounds like an argument an anti-vaccine layman might make. Pity the poor virologist who toils in the lab.
  • The Conflict Between the Academic and Non-Academic Worlds
    :up:

    I can add little to nothing. You have expressed your point of view - to which I agree - admirably.
  • Why being anti-work is not wrong.
    Assuming work is required for most - yes, a dreadful indignity of the human spirit - should a country, say the USA, make a top priority a minimum wage for any job must be enough for an individual to survive on their own - food, lodging, transportation, etc.?

    A beginning worker at McDonalds would not be forced to live at mom's home or share expenses with another for the necessities. And more men in the US age 30 and below do in fact live at their parent's home than was the case twenty years ago. More young women, too.

    Belonging to a much older generation I still believe in working one's way up, but housing is out of sight these days and gas is $3.50 - $4 a gallon. Prior to this three generations might live in the same house, and I see this returning, along with multiple families in one home.
  • Libertarians' open borders arguments and their application to Israel
    Why stop at open borders? If someone lives in the US, shouldn't they be allowed to vote - especially since they pay taxes? I bring this up as devil's advocate.
  • What is philosophy? What makes something philosophical?
    Scientific speculation is when two physicists discuss entanglement. This becomes philosophy when
    one of them mentions Kant.
  • Truthiness
    This is the best description of the truthiness of Euler's Identity I could muster. I didn't refer to any math textbook, nor did I consult a mathematician, the equation seems/feels true.TheMadFool

    Amazing. If mathematical life were only so simple. :roll:
  • What is philosophy? What makes something philosophical?
    As I might practice it, it's speculation. However, the literature shows that is a specific formal philosophical pursuit.
  • Is anyone else concerned with the ubiquitous use of undefined terms in philosophical discourse?
    Using as few words as possible is just as important as using the right words. Your argument could have been a lot clearer, less ambiguous, if you'd made the post a lot shorter.T Clark

    Philosophers love using words, the arrows in their quivers. And some, perhaps most, enjoy reading lengthy treatises. As an olde math person I admire brevity and conciseness, so, like T. Clark, I failed to make it through the OP, which, nevertheless, seems very well-written.

    The premises of many philosophical efforts frequently seem vague, to the point where, for example, the word "being" triggers my full retreat. "Metaphysics" also is confusing, and I am curious what Stanford's metaphysical laboratory can produce as enlightenment. Mostly it's just me.
  • What would happen if the internet went offline for 24hrs
    I only recently got a smart phone, but I don't use it much. Those damn small letters and having to move the text in order to read it. Nah.baker

    Fat fingers is a drawback. I try to avoid apps, but it keeps wanting them. Very demanding. :angry:
  • Number Sense
    Einstein's Special Relativity applies to physical objects. But General Relativity includes the subjective observer in the network, as a node in the whole pattern, by taking a god-like perspective, from outside the system looking inGnomon

    I think both special and general include observers. That's not the usual distinction. Accelerated motion and other features are considered in general.
  • With any luck, you'll grow old
    Well, as an elder - perhaps the elder at age 84 - on this forum, I'll make a few comments. But first, anyone older than me please speak up.

    They probably don't feel physically like age 25. When I say I feel young, I mean mentally, but what do I mean by that?
    Bitter Crank
    • Active curiosity (Important as one ages. Don't give up on the world.)
    • good memory (I wish. Images pop right up, but words describing them don't.)
    • ability to concentrate (Hopefully you've honed this over the years. If not, good luck.)
    • better intellectual skills - less overall stupidity (In politics recall what W. Churchill had to say about liberalism vs conservatism)
    • much more perspective (Depends if you've paid attention when younger.)
    • Sex drive at 75? Mercifully lessened (Speak for yourself, buddy!)
    .
  • The US $3.5 Trillion Reconciliation Bill
    I wonder how the making of concrete and steel will be powered?Xtrix

    Evraz steel mill in southern Colorado is constructing a massive array of solar panels to be the first steel mill in North America to incorporate solar power. This is nothing short of amazing. It's about fifteen miles from where I live.
  • The US $3.5 Trillion Reconciliation Bill
    Mr. Coal, Manchin, will be lobbied to take this outXtrix

    I wonder how the proposed desalinization plants for coastal California will be powered?
  • Number Sense
    I know it's trite, but imagine a maleable plastic doughnut being continuously deformed into a coffee cup. The notion of continuous transformations from one object to another is the fundamental topological characteristic. The more technical aspects involve open sets. If X is a non-empty set, a class T of subsets of X is called a topology on X provided (1) unions of sets in T are sets in T, and (2) intersections of finite collections of sets in T are sets in T.

    The study of topology begins with point-set topologies - and I have fond memories of being introduced to these in 1962 and teaching them during the last quarter of the past century - and proceeds to esoteric terrains I dare not tread.

    As G. F Simmons said, "A topological space can be thought of as a set from which has been swept away all structure irrelevant to the continuity of functions defined on it".
  • Number Sense
    One reason I wished to discuss the senses, specifically taste and smell, was they appeared to be qualitative (nonmathematical) instead of quantitative (mathematical)TheMadFool

    Qualitative does not imply nonmathematical. For example, it used to be said that topology is math without numbers, although that's not entirely true.
  • Math and Religion
    You seem to curiously relate politics to theology to mathematics... why though is beyond me, creating some odd mathematical mysticism that you seem to want our kids to learnTobias

    Good point.
  • Math and Religion
    That is speaking of the "one is the many" as monad means one and is represented as a circle.Athena

    I had not thought of monads apart from Leibniz's mathematical contributions. I now see that there is much more to the monad than I knew. Thanks for bringing this up. :cool:
  • How to envision quantum fields in physics?
    From lecture notes by Sourav Chatterjee, Stanford:

    Although quantum mechanics has been successful in
    explaining many microscopic phenomena which appear to be genuinely ran-
    dom (i.e., the randomness does not stem from the lack of information about
    initial condition, but it is inherent in the behavior of the particles), it is not
    a good theory for elementary particles, mainly for two reasons:

    • It does not fit well with special relativity, in that the Schr ̈odinger
    equation is not invariant under Lorentz transformations.
    • It does not allow creation or annihilation of particles.

    Since in lots of interesting phenomena (e.g., in colliders) particles travel at
    speeds comparable to the speed of light, and new particles appear after they
    collide, these aspects have to be taken into account.

    Quantum field theory (QFT) is supposed to describe these phenomena
    well, yet its mathematical foundations are shaky or non-existent. The fun-
    damental objects in quantum field theory are operator-valued distributions.
    An operator-valued distribution is an abstract object, which when integrated
    against a test function, yields a linear operator on a Hilbert space instead
    of a number.