The Nature of Exponential Growth

The COVID-19 virus is spreading exponentially fast.

Let me tell you a story: There was once a man who invented Chess. The King was so pleased, he offered the man a reward. “There are sixty four squares on a Chessboard,” said the man, "All I want is one grain of wheat for the first square, two for the second, four for the third, eight for the fourth, sixteen for the fifth, and so on.” The King eagerly agreed thinking it was a paltry price to pay, only to discover, to his horror, the nature of exponential growth. Essentially, on the very last square alone of the Chessboard, the King had to pay to the man, 9,220,000,000,000,000,000. or in words: nine quintillion, two hundred and twenty quadrillion, grains of wheat.

This presentation from MSNBC goes into exponential growth concerning COVID-19 more thoroughly.

Pythagoreans believed "all is number" and there is absolutely nothing else and Plato seems to agree with him with the Platonic solids and his theory of the forms. Interestingly Athena, I found this section in an old book of mine about Pythagoras' view of the cosmos. It took me over two hours to just type it out because my left hand needs surgery badly and I'm finding it very difficult to type at my age of 53.

Interestingly, the Pythagoreans used to believe the Earth was the centre of the Universe, but had to modify their beliefs in order to get it in sync with their mathematical demands. It is remarkably similar, although imperfectly, to Copernicus' view that came much, much later.

"Pythagorean musical and mathematical conceptions found their highest expression in the cosmological doctrine of the Music of the spheres. When Pythagoras declared that there is a universal harmony, a grand musical pattern, in the movements of the Universe, he was expressing, in his own style of concrete imagining, the conviction that rational law governs the universe. For to the Pythagorean mind, it must be remembered, music was identical with number, and number in turn was conceived geometrically. Consequently, since the circle and its perfection and simplicity made the strongest appeal to the unsophisticated mathematical sensibilities of the Greeks, the meaning of astronomical law became naturally affixed to it. There was no serious trouble conceiving the observed movements of the Sun, Moon and fix stars as basically circular, although the deviations between summer and winter required some explanation, but the apparent irregularities of the five known planets (Mercury, Venus, Mars, Jupiter and Saturn) created a serious difficulty that some kind of geometric pattern must exhibit itself in all of those movements made an article of faith for the Pythagoreans partly suggested by experience from observing the circular movements of the Sun, Moon and constellations, but in any case demanded as a guiding concept for the rational interpretation of whatever astronomical phenomena might be observed; to Pythagoras it appears that such astronomical order was conceived both geometrically and musically, that is by means of visual and auditory imagination combined, for it is recorded of him that on a few memorable occasions in his life he entered into the transcendental experience of actually hearing that celestial music. The general number theory gave rise also to a more particular astronomical result adding the orbits of the five known planets to those of the Sun and Moon and that of the fixed stars gave a total of eight orbits each of which must be conceived as basically circular or as somehow explainable in terms of a combination of circles. However eight was not a good Pythagorean number; the next number above it was ten or the Decad. Two more revolving bodies had therefore to be found and postulated; the need was met by conceiving of the Earth itself as a planet revolving about the same centre as that about which the Sun and other planets revolve and by postulating that behind the Earth on the side opposite to that on which the Greeks and all known peoples resided (Europe, Asia and Africa), there was a tenth revolving body which they called the counter-Earth. A cosmic centre had to be assumed which all ten orbits encircled, and this ultimate centre was conceived as the Central Fire. Of course inhabitants of the known Earth we're unable to see either the counter Earth or the Central Fire; this inability was explained by supposing that the Earth while revolving around the Central Fire kept its inhabited face turned away from the fire and the counter Earth with the result that they were perpetually invisible to Earth people. The hypothesis seems a curious one to contemporary habits of thought, but let it be considered that the Greeks lacking telescopes possess no example of a body rotating on its own axis, whereas experience did show them one example of a revolving body keeping one face towards and one face away from the centre of its orbit — namely the moon." (The Presocratics, Philip Wheelwright).

Dear daughter of Zeus, now I follow you.

I am a so-called "bipolar" man, and I possess knowledge.

I promise I will eventually view your presentation, but I'm frightened about what you are going to show me about food production. I can't help it!

Pythagoras thought number is the primary substance and I do not agree with him. Being, as described by Parmenides, is the primary substance. My father would always scold me because he thought I wasn't understanding basic arithmetic when I was only four years old and couldn't do so at that age because my mind wasn't prepared for it.

Dear child of Zeus, mathematics is the greatest knowledge we have.

Speaking of the Iliad, listen to this verse that Hector said,

No man will hurl me down to Death, against my fate.
And fate? No one alive has ever escaped it,
neither brave man nor coward, I tell you --
it's born with us the day that we were born. Iliad VI, 580

But look what happens later...

But the two Aeantes blazing in battle-fury
saw to Imbrius now...as two lions seizing a goat
from under guard of circling rip-tooth hounds,
lugging the carcass on through dense matted brush,
hoist it up from the earth in their big grinding jaws.
So the ramping, crested Aeantes hoisted Imbrius high,
stripping his gear in mid-air, and the Little Ajax,
raging over Amphimachus' death, lopped the head
from the corpse's limp neck and with one good heave
send it spinning into the milling fighters like a ball,
right at the feet of Hector, tumbling in the dust. Iliad XIII, 240

I don't know where I'm going with this Sir2u. Do you know?

Okay, this is a lame post. I do that from time to time, but I just loved the story. The Iliad was by far too violent and greedy and tells us who we really are Sir2u. As a human race, we have lost our sense of empathy and compassion. It is incredibly disappointing, but since I will be dead in about thirty years, at best, why should I worry?

There is no question. I just want to share it with you. Sir2u, I need to share it with you.

Seneca is as warm and cuddling as our mothers and fathers when we were only four years old, no matter how awful things become. As that provided to children who perished aboard the Titanic. :smile:

I agree with you; homelessness is on the rise and it is only going to get worse along with hunger, painful drug addictions, lots of suffering, and apathy among the rich who only find worth in charity if they get to put their name on it. But I can identify two serious problems we need to address. They are our undying, relentless and worse uncritical love of democracy and capitalism.

The ability to know both what is and what ought to be, the essence of what we call morality — TheMadFool

Splendid idea! So all we need to know now is what is and more particularly, what ought to be. Especially because we are talented at knowing what the former is from experience, but pathetic at understanding our future. Do you have any ideas?

I apologize for the confusion.

Living in the moment is disingenuous because you are giving up on a part that is essentially human. — ChatteringMonkey

Narrowly viewing Seneca's philosophy and advice as simply "living in the moment," is disingenuous. How should it matter if your plans and hopes for the future are satisfied or ends suddenly today by an untimely death?

Seneca had a friend named Marcia who lost a young son and became overwhelmed with melancholy; she wished not to live anymore. Seneca came to her aid by taking her on a brief tour of the troubled Earth before she was born, with its beauty and horror, and asked her to weight up whether she would want to step into such a life.

I'm going to take his argument one step further. Suppose you did actually have that choice, but I add the condition that once you step into it, there will be no end to it. You will live forever! Now would you choose to be born?

how can things be meaningful if all things are impermanent or temporal. — runbounder

Stop complaining about the temporary nature of life as if it were a bad thing!

I have felt exactly the same way you do and you do not have to stay there.

As soon as you embrace it, you will discover the things that frighten you the most are just phantoms and nothing to worry about. :smile:

Sir, I found what you wrote so funny, I'm having serious trouble typing this as we speak.

You can clearly notice that unbelievers are gradually but surely losing the ability to form families and to reproduce... children are a gift from God. — alcontali

. And your reply,

I am a non believer, and I have no problems reproducing! — Sir2u

But given the state of our planet, with overconsumption of resources especially our food, and we are limited in our abilities to manufacture it on our farms, combined with climate change, too many children is God's curse on us and he delights in our suffering!

How am I unable or unqualified to judge God based upon what we think God is through Scripture? Consider your argument:

1 Thessalonians 5:21 Test all things; hold fast what is good.

, and you asking whether that is true or whether

you let someone else do your judging for you.

. But another important part of the Bible in Matthew 4 says, Satan was tempting Jesus to throw himself down from a height and he replied, "Do not put the Lord your God to the test."

I see little difference between "religious fanaticism" and partisan politics, for example.

. I cannot see any difference either.

Democracy will only work when voters use their ability to reason and not how to satisfy their desires beyond basic needs. Last night, in Donald Trump's State of the Union Address, he spoke mostly about how his party has provided them with economic growth; I think it's simply a matter of post-hoc ergo proper-hoc fallacy and that politicians really have very little power to alter the economy that seems to have a mind of its own. Suppose he really did improve the economy, and he says he will provide more of it if elected. Obviously Trump's logic is people want more of that and the electorate will vote for him on those grounds, like a candy store clerk, despite the objection of the doctor that says "we should take the candy away before they harm themselves with excessive amounts of it." Just like a parent taking candy or another dangerous thing away from a child, of course they are going to cry about it.

Something just struck me profoundly. When I was a young child, I did indeed believe in ghosts and they were not like Casper the Friendly ghost, but rather from watching the Night Stalker because my father did not have enough sense to put me to bed at a reasonable hour. :wink:

As a result, I had problems getting to sleep for understandable reasons and my fear was genuine; it's the same fear I have today but the latter is justifiable. When I complained to my mother about the ghosts, she tersely said to me "there are no such things as ghosts!" To my disappointment I did not find that convincing.

Suppose some adult complains he fears ghosts are haunting him, I'd say to him that if a horrible and effective assassin was trying to kill you, and then convince him the assassin is now dead, would that person fear his ghost is going to be a problem?

But that doesn't actually contradict it, that just bites the bullet.

. Yes, I agree with you and of course I haven't proven anything and I'm not trying to. I just think what most people believe "God is" is incorrect and thus cannot be instantiated. A God that is completely uninterested in our well being is much more reasonable. Also, I believe even the "hard core" atheists like Richard Dawkins, would be much happier if people adopted that kind of theism that denies the "power of prayer," an afterlife, miracles and one that judges us by punishing the evil and helping the good. For they will only to be disappointed when they discover the evil usually fare better than the good. Look at what Donald J. Trump is getting away with.

PI is indeed the ratio of the circumference divided by its diameter. But if you set the diameter equal to 1, and set the circumference to 3, you will underestimate its actual value of 3.14159... and if you set the circumference to 4, you will overestimate its actual value. To date, we have calculated it to well over 16 trillion digits and tried using many computer algorithms to try and find a pattern and nobody has been successful. I sometimes wonder why mathematicians bother in this silly endeavour.

I cannot answer your question about special relativity, but I can tell you not to bring up anything "philosophical" with scientists because they despise philosophers . If you ask them why, it's almost always because of the harm philosophy has caused the pursuit of truth and they mention Aristotle to support their claim. Most scientists I've talked to complain that Aristotle thought light bodies fall slower than heavy bodies. I replied that wasn't the true reason why the Catholic Church rejected Galileo's gravity claim. It was because he and Copernicus showed, with a heliocentric model, the book of Joshua is nothing but mumbo jumbo. This all could have been remedied if the Church would finally admit the Bible was only written by ordinary people and some of them were incredibly stupid.

I've tried to explain to them that Aristotle practically invented formal logic that we still use today, however he did frequently make mistakes. Unfortunately because society, namely the Church, refused to believe he could possibly be wrong, it got us into trouble. Interestingly, it was philosophy, through the works of Sextus Empiricus and later by Rene Descartes for example, and not science that "put Aristotle in his place."

I have learned through experience to not talk about philosophy with scientists even though I love science as much as philosophy. Scientists do not see it that way and you'll be happier if you do not mention philosophy at all.

Yet, when I point out the atomic bomb is a product of scientific work and how it has seriously threatened humanity, scientists refuse to accept any responsibility and instead say that it is humanities' misuse of science that is the problem. Similarly, using their logic, it's not gun manufacturers that are the problem in society, but rather the misuse of the technology by people.

Here's another example, science is responsible for producing the multitude of ways to consume fossil fuels and now humanity is in very grave danger from climate change. Once again, scientists refuse to accept any responsibility for this and then complain that humanity refuses to accept science that says greenhouse gasses are the problem. But if you ask a philosopher what the problem is, they will most likely say people do not usually act in accordance with reason but instead act they way they do because of wants and desires, and thus they do want to give up their science (e.g. cars, electrical power, energy to heat their homes, etc.)

Scientists also do not want to hear that Albert Einstein was a huge fan of Baruch Spinoza.

I have a question for you. I was told acceleration or the application of force on the male twin is what solves the twin paradox. Please explain.

Hi, rational is derived from the Latin word 'reckoning' or in accordance with reason. Because of the secretive nature of the Pythagorean School, we don't know what they called it. The sqrt(2) and many others are irrational in the sense they cannot be expressed as a ratio of integers. Since, according to the Pythagoreans, all numbers must be expressible that way they falsify the claim the Pythagoreans held dearly in their hearts. Similarly, Galileo's and Copernicus' work was declared irrational by the Catholic Church because it means Aristotle and the book of Joshua are wrong, and the Earth is not the centre of the Universe and humanity isn't as significant as we thought we were.

I corrected a logical error in the proof and posted it above.

The story is apocryphal.

Of course it is @StreetlightX but it's entertaining.

It's just a legendary story and we really don't know what exactly happened because their school was so secretive in nature. I hope @Metaphysician Undercover will forgive me. :wink:

After all this discussion, I'm starting to reject my claim that Zeno's paradox can be solved by our inability to count and measure things. I'll think about this more at a later time.

I'm not saying mathematics is illogical or wrong and thus theories about reality are illogical or wrong. Einstein's equation E=mc^2 correctly predicts how much energy will be produced from a certain amount of matter. What it cannot do is tell you how much matter is in a reactor say. The actual number must be estimated by us and then plugged into the equation to obtain the exact amount of energy based on that estimate. That is why I say reality is hard to fit into mathematics or mathematics into reality.

I'm saying a number "exists" only if it can be instantiated by something in reality. If many thing exist, then one cannot be instantiated by anything.

Suppose there is one and only one thing in the Universe and absolutely nothing else. Then the only number that exists is one. But in that case one is a meaningless predicate because everything is one. But if you divide that one thing into two pieces, then two exists and a half exists but one no longer exists. If we divide the one into three pieces, then three exists and a third exists, but both one and two no longer exists or any other number. If you object and say there are two (1/3) and one (1/3), I can say 2(1/3) is not the same as 2(1/2) that we used when we defined what two is and 1/3 is not the same as one when we defined what one is. I am certainly not saying mathematics is illogical or not useful. I'm saying things in reality are not numbers and I do not agree with Pythagoras that all is numbers. AFTER THOUGHT: okay, I confess that argument is lame, but all I'm trying to say is while it's easy to say there are six chairs at the table, no more no less, and if there are ten people attending the dinner, we need to get four more. However, it is possible, abet unlikely, we miscounted them. I'm almost certain E=mc^2 is exactly true, but it won't tell you how much matter is in a reactor that is converted to energy. That figure must be estimated by us and the equation will tell us exactly how much energy will be released based on that estimate. That is why I say it's hard to go from mathematical laws and concepts to reality and back again.

Infinity is not a real number because all real numbers have a definite magnitude or value whereas infinity does not. Infinity is always greater than any particular real number. Here's what I mean: the limit of y=1/x^2 as x "tends to infinity" is zero. I'm very unhappy with the "tends to infinity" part because it gives the feeling that x is moving to the right on the real number line with some kind of limited speed like a moving automobile. That is why Zeno's paradox arises because numbers can be divided infinitely and if that is the case, motion is impossible because the body must somehow traverse infinitely many numbers in a limited amount of time. That would mean movement amounts to saying some real thing pops out of existence at some point and then, over time, pops into existence at another point which is utterly absurd.

People frequently argue that problem has been solved by the concept of a limit. But that is not the case because unlike things in nature, there is no speed limit in mathematics. All operations in mathematics, counting 1, 2, 3, etc. happen instantaneously. x doesn't tend to infinity but is infinity. In the function above, x will never reach the x axis for any real value of x no matter how large it is, the moment you say x is some real number, essentially you have stopped "tending to infinity." Here is my solution to Zeno's paradox, things that happen in reality like motion do not exactly correspond to things in mathematics. Suppose you have a rod of a finite length. You cannot measure it with a ruler to determine its mathematical length exactly and mathematics always demands things be exact or it is just an estimate.

All the rules of mathematics for real numbers do not transfer over to arithmetic involving infinity. For example, for real numbers except zero (not all the rules in arithmetic apply to zero either for you cannot divide by it) you cannot perform an operation on one side of the equation only and expect to obtain a true result. Whereas (infinity = infinity) and (infinity + infinity) = infinity are both true.

Thank you so much for the link! I'll watch it later today. I love Parmenides' thoughts and are the basis for much of mine.

1/(positive infinity)=1/(negative infinity). that equation is the same as 0=0 and zero does not have any polarity.