Logic and First Principles of right reason Mathematics Selective Hyperskepticism

Simple demonstrations of how structure and quantity are embedded in the world

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As there seems to be resistance to the point that the world embeds structure and quantity (thus, mathematical features) I think it is useful to provide some simple reminders.

The Egyptian rope trick and the 3-4-5 Pythagorean triplet, thus a right angle forced through a numerical relationship (and note the power of the number twelve again):

Lego bricks demonstrating the Pythagorean relationship — notice, number theory connexions and the natural interpretation of “squaring”:

Also, notice a Mobius strip cutting exercise:

In none of these cases is the result dependent on our creating a mathematical model or an axiomatisation. The results are objective, factual, embedded in the world and in fact helped to constrain how Mathematical systems were axiomatised. END

In none of these cases is the result dependent on our creating a mathematical model or an axiomatisation. The results are objective, factual, embedded in the world and in fact helped to constrain how Mathematical systems were axiomatised. END

PS: Dr Tokieda’s lecture on Mobius strips (with demonstrations):

Lecture series, here.

8 Replies to “Simple demonstrations of how structure and quantity are embedded in the world

  1. 1
    kairosfocus says:

    Simple demonstrations of how structure and quantity are embedded in the world

    –> our modelling exercises (including axiomatisation of systems) will be constrained by need to conform to a body of manifest mathematical facts.

  2. 2
    hazel says:

    Again? 🙂

  3. 3
    Ed George says:

    Isn’t there a phrase that involves violence against a dead horse that explains endurance of this topic? 🙂

  4. 4
    hazel says:

    Yes. I in fact posted that, and then deleted it. I figured it was beating a dead horse to point out that someone was beating a dead horse. There is nothing worse than infinite regresses! 🙂

  5. 5
    Jammer says:

    The dead horse will have to continue being beaten until reality deniers stop, well . . . denying reality.

    It could be a while.

  6. 6
    hazel says:

    No one is denying reality. The physical world is quite real.

  7. 7
    kairosfocus says:

    H, the physical world is real and demonstrates in convincing ways that it embeds certain forms of structure and quantity. KF

    PS: Here is a relevant Scripture:

    Ps 32:8 I will instruct you and teach you in the way you should go;
    I will counsel you [who are willing to learn] with My eye upon you.
    9 Do not be like the horse or like the mule which have no understanding,
    Whose trappings include bridle and rein to hold them in check,
    Otherwise they will not come near to you. [AMP]

    Then, there is pons asinorum . . .

    THE PONS ASINORUM; OR, THE ASSES’
    BRIDGE.

    SONG, WRITTEN IN MR. J. MILLER’S MATHEMAT-
    ICAL CLASS.

    As Miller’s Hussars marched up to the wars,
    With their captain in person before ’em ;
    It happened one day that they met on their way,
    With the dangerous Pons Asinorum !*

    Now see the bold band, each a sword in his hand,
    And his Euclid for target before him ;
    Not a soul of them all could the dangers appall
    Of the hazardous Pons Asinorum !

    While the streamers wide flew, and the loud trum-
    pets blew,

    And the drum beat responsive before ’em ;

    Then Miller their chief thus harangued them in
    brief,

    ‘Bout the dangerous Pons Asinorum !

    tl My soldiers,” said he, ” though dangers there be,
    Yet behave with a proper decorum ;
    Dismiss ev’ry fear, and with boldness draw near
    To the dangerous Pons Asinorum /”

    Now it chanced in the van stood a comical man,
    Who, as Miller strode bravely before him,

    * Fifth Proposition of the First Book of Euclid.

    THE FIRST OF MAY, 1793. 3T.1

    To his SORROW soon found that his brains were

    wheeled round,
    As he marched to the Pans Asinorum !

    O sorrowful wight, how sad was his plight,

    When he looked at the Pons Asinorum !

    Soon the flight took his heels, like a drunkard he

    reels,
    And his head flew like thunder before him.

    So rude was the jump, as the mortal fell plump,
    That not Miller himself could restore him ;
    So his comrades were left, of ” Plumbano ” bereft r .
    O pitiful plight to deplore him !

    1791.

  8. 8
    LoneCycler says:

    Structure and quantity are embedded in our world in ways both subtle and salient. The arguments for or against that here at UD seem esoteric and carried out by people that spend their time in front of a keyboard thinking about stuff. Not really my cuppa though I have to admit I’m still trying to wrap my mind around the mobius strip example.

    Modern technology in western civilization insulates people from nature. It seems doubtful anyone here expounding on what nature contains or not has spent much time in the trackless green world hunting wild trout. Or prospecting acres of pecan groves for truffles. I am likely the only person that frequents UD that is still suffering the results of bulling through a mile of briar patches and palmettos to locate a lost gun dog last mont. Which was a complete waste of time as the dog made it back to its owner 25 miles away without help from anyone – but I digress.

    From their climate controlled office environment people claim perfect circles don’t exist in nature. Have you seen an ice halo around the Sun? Our Sun is as close to being a perfect sphere as anyone has found, its oblate error being the same as viewing the width of a human hair at a mile. Halos around the Sun have the same error, with additional error due to atmospheric refraction, that is, an error undetectable by the human eye. Halos can even appear on the ground: https://www.atoptics.co.uk/fz868.htm

    Halos are the result of the Sun’s rays being refracted 22 degrees through a hexagonal ice crystal. Water always freezes into this crystalline structure. What do you suppose ancient people thought and what would they know about halos? “The only time I see this is when it’s really @!#$ cold” is my guess. And they would attribute them to the supernatural. Halos were used in many ancient cultures to indicate divinity of their rulers from Greece to India to China to the Romans who passed it on to Christianity. Rainbows are arcs, not complete circles, but their circular nature is also evident to even a casual observer. These would have also been recognized as part of a circle by ancient people.

    You can’t touch a halo but you can comprehend what they are. Things like this exist in the world and they are here for us to observe, wonder about, and prompt us to investigate them and learn. It is human nature. It is the process of investigating and learning new things that leads in a direction the Designer intended. We were given minds and thinking skills for a reason. Not by an accident which is what some would like us to believe.

    The sphere? https://pxhere.com/en/photo/838369

    See also eggs, pearls and other kinds of fruit. Let’s not forget the mysterious stone spheres of Costa Rica. Just because there are no “perfect” spheres it did not hinder attempts by some people to manufacture them. Mysterious? Anyone that’s seen the beginning of Raiders of the Lost Ark will know what they were used for. Perfect? No. Close enough? I think so.

    Over human history people have used their minds to discover embedded structure. In a world lit only by fire the night time sky would have made a great impression on ancient humans. The night sky changes only slightly each night but over a year’s time the changes add up. And then it repeats itself again. Like clockwork. This is a characteristic of the world you won’t notice being indoors all of your life.

    Ancient people’s TV and cable was sitting around on comfortable logs in the dark telling stories about the stars and the images they thought they saw in them. People noticed the Moon ruled the night time sky, except when it didn’t, and developed calendars based on the Moon phases. The problem with that is the Moon is not in cycle with the Sun and if you keep using it to measure dates you’ll wind up planting just in time to harvest in the dead of winter and your clan/tribe/harem dies of starvation. The oldest lunar observation site found so far is Warren Field in Scotland. Warren Field has artifacts that could be used to correct a lunar calendar by resetting it at the midwinter solstice. If you can correct your lunar calendar by using the Sun there won’t be any ill effects and if you like your clan/tribe/harem you can keep them.

    Making the correction at midwinter is smart because what people really wanted to know was how long it would be before spring arrived. In some places these days it is little more than a joke as extended winter is just an inconvenience not a life or death matter. See Punxsutawney Phil the Pennsylvania ground hog and the event organized around his prediction. In ancient time you got the math right the first time or else you and yours died.

    Constructed around 8,000 BC Warren Field predates known Middle East sites by around 5,000 years. It predates the entire Pythagorian/Vegetarian/People for The Ethical Treatment of Animals period in the Mediterranean by around 7,500 years. People noticed structure and quantity in the world and used math to accomplish things a very long time before Greeks wearing togas came along.

    Pythagorus was known as a shyster by his contemporaries but is today revered for a formula he wasn’t the first to discover or prove. Not content he developed a cult that required people eat what he thought they should eat, live the way he thought they should live and in general control whatever other aspects of their lives he thought needed control. Not satisfied with teaching math many higher education professionals today are similarly bent with their “woke” social justice post-post-modern nihilistic urges to tell people what they should think and how they should act. I think I just discovered why many think Pythagoras was a big deal when he really wasn’t.

    The measurement of time was probably not the first thing measured by humans. The history of human use of math I find interesting. One way we can say for certain math was known and used is when we discover ancient people were measuring something. Time, distance, how many pots of beer they have to sell, etc. You can’t measure something without math. At the very least when something is measured you arrive at a conclusion that it is more, less or just what you wanted, and this requires comparison with a known standard or quantity through the use of math.

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