Essay Abstract

The mathematics we have inherited from the Ancient Greeks is bare of "duration" that is, timeless. If asked about the maths counting event "1 1=2" all would say that "duration" isn't involved, end of story, only physical events have "duration". This obviously is the most profound difference between mathematics and physics. Maths events are bare of "duration" while physical events have "duration". What if a wonderful trick could be found to give maths events duration? And what if we could match these durations to physical events, then that would be a great truth!

Author Bio

Just interested in physics.

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Hi Juoko,

I had never heard of Sorites Paradox so thanks for bringing it to my attention. At first, I thought the paradox only had to do with vagueness and that if one defined how many grains of sand constituted a heap, the paradox would go away. (It also reminded me how some people think that their one vote won't change an election from a loss to a win, just like a grain of sand won't change a non-heap to a heap.) But after thinking a little more, I wondered if there could still remain a paradox in a continuous model. Suppose a continuous substance was considered to be a heap, and half of the substance was considered definitely well below the threshold of what constituted a heap. Could one ever identify the crossover point where the substance changes? Could one develop an algorithm for identifying that point where the distinction changes? ...The boundary of distinction. I was a little confused by some of your essay, but I was wondering if you have thought about time and change from both a continuous and discrete perspective.

Please check out my Digital Physics movie essay if you get the chance.

Thanks,

Jon

    Wonderful new viewpoint. You and Ojo should talk.

    Sorite paradox seems related to Zeno's paradox. In a conversation with Ojo, I concluded division was an illegal math physics operation. That is, multiplication is the result of multiple additions. Division and Zeno's paradox must be a result of multiple subtractions. This solves Zeno but, as you point out, goes directly into Sorite.

    A clock has been defined as duration between events such as a tick of a pendulum swing. Recently, the clock is dependent on the decay of atoms that decay one atom at a time - the sand heap. I think this is fundamental as Zeno's paradox. My solution is to recognize that the ``heap'' depends on the definition of a heap in terms of number of grains of sand. Thus, a tick occurs when the grain falls that amounts to the defined number. As I mentioned in my essay

    in the conversation about time, this definition is subject to many, many unknowns as are the dropping of the sand grains. Thus, duration accuracy has been increased, has duration repeatability been increased? Perhaps, not. Physics is still searching for a better standard. But, the issue is not math, it's a quest for a standard.

    To repeat, at the core is the Zeno's and Sorite paradoxes.

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      • Post #4

      I have thought deeply about your comments and have attached a long reply. The last couple of pages would be of most interest to you. A continuous version of the Sorites (for example tall going to short) has been discussed in an excellent paper by Weber, Z. and Colyvan, M., 2010. 'A topological sorites', The Journal of Philosophy, 107: 311-325 check it out if interested. In the attachment I go through the whole argument again and have added some more notes about what the past, the present and the future are, and have added some notes about the "now". The continuous version involves a huge change of scale but guarantees that the continuous version goes to the discrete version within time.

      Thank you for your interest and insightful question. Yours HarriAttachment #1: response_one_to_competition.pdf

      Dear John thanks for the nice comment about the idea in the essay. Yes I think that Zeno's paradox and Sorites Paradox are related but I think it will take a lot of thought to fully work out the connections. Zeno's paradox seems to be about going from a discrete movement to a continuous movement of zero length so a continuous form of sorites might be helpful. The sorites in the paper is about time being discrete because I make Plank's constant a cyclic-measuring-device to work out what are the invariant events of reality. And clearly the endpoints are spin 1/2 invariants and the grains are integer spin invariants. That is the invariant events are microscopic not macroscopic events like "the event of the universe" or "the event of your life" since clearly there are temporally dependent sub-events like your 18th birthday event etc. for macroscopic events.

      Yes it about what standard you use and in this paper Plank's constant is considered as the base clock for reality.

      Thanks for the heads-up about Ojo. I will read yours and Ojo papers shortly and comment on them.

      I have attached a pdf that goes into more detail about the ideas and the last page has the continuous version of Sorites Paradox.

      Yours HarriAttachment #1: 1_response_one_to_competition.pdf

      Dear Harri,

      One of the positive aspects of these yearly essay competition is the possibility of learning something new. I have you to thank for bringing Sorites paradox to the table. Very interesting and I am learning about it for the first time. I will therefore have to give it some more thought.

      But for starters it appears to do with 'definition'. Among questions running through my mind are:

      - what is a heap?

      - what is a grain of sand?

      - is a grain of sand, a heap, i.e. a tiny heap?

      - is a heap, a big grain of sand?

      - is a heap made of grains of sand alone, or along with something else, e.g. air?

      - when a grain is removed, is it removed along with any other thing?

      - what does 'remove' mean? Can things be separated, and if so by what? If by nothing, then it means they have not been separated or 'removed'. If by something, from whence did that something come? Or was the something always there?

      Following the issue of structural definition, is a question of functional definition. That is, has any change being made when a grain of sand is removed from a heap? If a heap remains a heap, then for the hour-glass example, time has not changed. If another grain is removed still time has not changed. But then a sum of zero changes of time must equal zero, yet when the hour glass is emptied a duration of time has definitely passed. It therefore appears inevitable that removal of a grain of sand from a heap has changed that heap. If you like changed to 'Heap - 1'. Removing another grain can be represented as ('Heap - 1') - 1, etc.

      I therefore agree, that the paradox suggests that there must be a limit to the addition or subtraction from a heap without changing the definition of heap. In this way Sorites paradox must admit of events.

      Your essay and the paradox is one deserving of being read again and again. A "heap" of value to gain.

      Wishing you the best in the competition also,

      Akinbo

        Akinbo Thank you so much for your kind words. I never realised that Sorties Paradox wasn't well known within the physics community.

        About your definition questions

        The equations I developed account for these questions since we use symbols for a heap т--П, a non-heap т--Л, and the grains т--' the quanta of the cycle. Each will have a different idea of "how many grains make a heap" yet if all people use the same symbols for the variables then the duration of a heap cycle is [т--П,т--Л]=iт--', that is, all will agree with this equation for their heap of sand. So [т--П,т--Л]=iт--' is an invariant. Later it is shown by use of the SAU matrix we must obtain six т--П spin-1/2 leptons and six т--Л spin-1/2 quarks and six т--' integral spin bosons and all will agree with these temporal invariants.

        You have grasped the paradox most excellently with your analysis "That is, has any change being made when a grain of sand is removed from a heap? If a heap remains a heap, then for the hour-glass example, time has not changed.... "If another grain is removed still time has not changed. But then a sum of zero changes of time must equal zero, yet when the hour glass is emptied a duration of time has definitely passed." Encasing the Sorites within a sand glass really makes the paradox extremely stark.

        A Temporal Sorites really challenges the most basic ideas about duration, time, the flow of time, what are events. And why should the paradox give us invariants that are so similar to the particles of nature, is mysterious but exciting when you think about it.

        Thank you Akinbo so much for your kind words and succinct thoughts about the essay. Yours Harri

        Dear Akinbo

        I have been thinking about your questions.

        In the literature the sorites (the paradox is usually written with a small "s") comes in three forms.

        1. Conditional (C) sorites -- how are the predicates (heap & non-heap) related to each other and to the duration of the journey of the grains?

        2. Mathematical Induction (MI) sorites -- how is the first step of MI related to the last step (for the grains) of the journey which doesn't end in a grain but a heap?

        3. Line-drawing (LD) sorites -- at which number of steps (i.e. which number i of grains) does the change happen or when does MI fail? Or by the least number principle (equivalent to the principle of mathematical induction) there must a point (a line in the sand) when we go from heap to non-heap.

        The C sorites equation is [т--П,т--Л] = duration of the journey of the grains in H = iт--'

        The MI sorites is т--ЛтЖ"т--'тЖ"т--П the top half of H with "phase" of e+iт--'

        The LD sorites is т--ПтЖ"т--'тЖ"т--Л the bottom half of H with "phase" of e-iт--'

        Such that = the interference patterns for "time": its flow, the past, the present, the future and the "now". Where is the state vector for MI.

        sorry for some reason the last post didn't post correctly

        Dear Akinbo

        I have been thinking about your questions.

        In the literature the sorites (the paradox is usually written with a small "s") comes in three forms.

        1. Conditional (C) sorites -- how are the predicates (heap & non-heap) related to each other and to the duration of the journey of the grains?

        2. Mathematical Induction (MI) sorites -- how is the first step of MI related to the last step (for the grains) of the journey which doesn't end in a grain but a heap?

        3. Line-drawing (LD) sorites -- at which number of steps (i.e. which number i of grains) does the change happen or when does MI fail? Or by the least number principle (equivalent to the principle of mathematical induction) there must a point (a line in the sand) when we go from heap to non-heap.

        The C sorites equation is [т--П,т--Л] = duration of the journey of the grains in H = iт--'

        The LD sorites is т--ПтЖ"т--'тЖ"т--Л the top half of H with "phase" of e-iт--'

        The MI sorites is т--ЛтЖ"т--'тЖ"т--П the bottom half of H with "phase" of e+iт--'

        Such that = the interference patterns for "time": its "flow", the past, the present, the future, and the "now". Where is the state vector for MI.

        14 days later

        If this Universe is only "physics" bound how you would do the numbering and astronomical calculations?

        -Regards,

        Miss. Sujatha Jagannathan

        9 days later

        Dear Juoko,

        I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

        All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

        Joe Fisher

        Thanks for the sorites paradox and the hourglass metaphor. It took me a while to see the hourglass symbology and your essay is very clever to combine that with the paradox of partials. When does time begin or end? When does an event begin or end? When is an object an object?

        While questions about space and motion seem to have obvious and intuitive answers, just like with Zeno, questions about space and motion have irreducible paradoxes as you aptly show for sorites as well.

        The solution is to recognize heaps as objects, as you have done, and as an object, a heap exists in time given some action. Your metaphor has an implicit gravity force as well as an agent to switch the hourglass on and off, starting and stopping time, but the universe does not stop and start quite like this.

        You have time as the grain by grain decay of a heap of sand, which are the two dimensions of time. You build your objects with three hourglasses, which of course mirrors the way that charges and neutrals are both bound by exchanges of of a third particle in all objects of matter. This is a very apt metaphor for all objects.

        Since I don't consider 1+1=2 as timeless since it takes time to write it, to learn it, to think it, and it exists as an object of our brain matter as well as a neural packet of our aware matter. Thinking requires energy and energy is matter and action over time. So I do not buy into your timeless premise.

        Also, since you have a supernatural agent turning your hourglasses on and off, the question you pose is simply resolvable. The object begins when your agent turns it on. Your symbolic algebra is a very clever restatement of reality.

        2.0, entertaining

        1.0, well written

        0.5, understandable

        2.0, relevance to theme

        5.5

        a year later

        Harri, I just found and am about to read your paper "A Theory of Events" and already have several comments and questions. If you find this note and would like to reconnect (I assume this is the Harri who knows me from Sydney and Calgary), please follow up with me at: seinphil@shaw.ca Much to discuss. I've just finished writing a book, "A World of Possibility: Toward a Quantum Ontology", which may well harmonize with your ToE. Best, Phil

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