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Remove the Mysticism from Mathematics!
#26

Remove the Mysticism from Mathematics!
I'm starting to think we are in the presence of a Misunderstood GeniusTM. With a YouTube account.
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#27

Remove the Mysticism from Mathematics!
(02-25-2021, 07:06 PM)trdsf Wrote: ...I'm going to refer you to Episode 5 of Simon Singh's Numbers, a BBC Radio podcast.  I recommend the whole series, actually -- they're all short, about 15 minutes long, covering one idea in number theory.

Thank you for the link.       Thumbs Up
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#28

Remove the Mysticism from Mathematics!
Also, I'm wondering if you're aware of harmonics in gravitational relationships. Stabilities can arise out of chaos. Is the math describing that phenomenon "metaphysical"? Or is it simply descriptive of a natural process?
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#29

Remove the Mysticism from Mathematics!
(02-25-2021, 08:55 PM)trdsf Wrote:
(02-25-2021, 07:21 PM)Extreme Finitism Wrote:
(02-25-2021, 06:33 PM)trdsf Wrote: Um, no you can't.  A logic system that only proves one statement of mathematical truth isn't really a logic system since it's not free to prove or disprove other mathematical truths.

In a nutshell, here's why mathematics is not metaphysical -- not that it is physical, but that it's not metaphysical:

Take one equation and give it to 50 mathematicians.  You will get the same answer within any degree of accuracy you care to set, and you'll get it 50 times (absent human error).

Ask 50 theologians what the Old Testament book of Micah means to the modern mainline Protestant movement, or ask 50 astrologers to tell you the characteristics of a person born at a specific place and time, and not only will you not get the same answer 50 times, you'll get up to 50 different answers, many of which are mutually exclusive.

Numbers can't have arbitrary values.  That's part of what makes them numbers.  You can't redefine one to mean one and a half because then it's just not one anymore.  And I'm not talking about the word or the symbol we use, I'm talking about the concept -- philosophical or otherwise -- of 'one-ness'.  There doesn't need to be a concrete object I can point to that is the abstract essence of 'one' for it to be meaningful, useful, and non-metaphysical.  Physicists and chemists use the ideal gas law all the time.  That doesn't mean an ideal gas is a real thing, nor does it invalidate the law.


Um, yes you can. This is exactly what happened with the stupid idea of 'real numbers'. Simon Stevin came up with the idea of unending decimals in 1594 and over 200 years later various mathematicians eventually concocted a system of definitions and rules revolving around the idea of 'limits' specifically devised so that we could 'prove' things like the completeness of the reals and that 0.999... equals 1. There would otherwise be no justification for the imaginary number line (aka the continuum) that is infinitely thin and infinitely divisible and which goes from minus infinity to plus infinity. We can also supposedly talk about the 'cardinality' (another meaningless fairy tale concept) whereby there are just as many infinitely small so-called points (whatever they are!) between 0 and 1 as there are between 0 and 2. To anyone not fooled by the fairy tale, this is obviously a contradiction even if everything that came before it wasn't. But no, we are allowed to include an axiom of infinity which simply declares that an infinite set exists and so infinity MUST make sense because we have defined it to be in our system! 

My daughter is a mathematician and she often gets different answers to other mathematicians. This is often because high level maths questions can be so obscure and unclear that even mathematicians can't easily agree on the 'meaning' behind these abstract non-physical concepts.

Next you talk about not being able to redefine the 'concept' of 'one-ness' and you claim to not need a concrete object to point to. But in order to share meaning with another human you need to explain what you mean by 'one-ness' and this will inevitably require references to things in our shared physical reality that another human can relate to. Also this 'concept of one-ness' is physical in nature in that it only exist if a working brain is processing data within the chemistry of the brain that your brain interprets as being 'the concept of one-ness'. It is all physical. To think that 'one-ness' is out there in the universe is to believe in metaphysics. I have another video about this (in which I talk about the idea that 'three-ness' and patterns are somehow out there in the universe)...

Does Infinity Exist? No, Infinity Does Not Exist (The Disbeliever, Part 5)
{link removed}


Well done, you have followed the advice in my 'part 10' video to the letter. Go to the top of the infinitely large class and be careful not to fall off when you reach the end. Dance
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#30

Remove the Mysticism from Mathematics!
(02-25-2021, 09:06 PM)Finite Monkeys Wrote: I'm starting to think we are in the presence of a Misunderstood GeniusTM. With a YouTube account.

That would be "yet another" Misunderstood GeniusTM ... who makes YouTubes.
How many of these nut-cases have we seen over the years ?
Countless.
This one can't even begin to discuss the baisc general philosophy of the subject.
He says "nobody knows" .... but wait. He certainly does.
Yawn.
He came here to peddle his videos.
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#31

Remove the Mysticism from Mathematics!
Yeah, I don't remember hearing anything about a random YouTuber winning the Fields Medal for upending all of 20th century mathematics.  I think we've got a plain old garden variety crank, of the order of someone who thinks you can make Relativity consistent with Quantum Mechanics by tacking ±ħ onto E=mc2.
"Aliens?  Us?  Is this one of your Earth jokes?"  -- Kro-Bar, The Lost Skeleton of Cadavra
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#32

Remove the Mysticism from Mathematics!
As a back-end developer supporting line-of-business applications, I have never needed anything beyond basic high school algebra (sums, averages, means, and percentages, mostly) and my biggest mathematical challenge is to avoid rounding errors. This is slowly changing, and if my working life ends up extending much beyond the next five years, I'm going to be forced to stop ignoring discrete math and some of the headier concepts in statistics, because machine learning is infiltrating basically everything, even in my world.

That said, the value of mathematics is that it is reproducible and useful at accurately predicting, explaining and describing lived experience. I am not perturbed, nor find it woo-ish, that if you have infinite precision floating point numbers, you can divide by two forever and never reach zero, or that one can have infinite loops or recursions with simple integers.

Then there's the universe, which may or may not go on forever (may or may not be infinite) but it is plenty large enough that "infinite" is a useful description relative to human scale. Nothing woo-ish about that. In fact if I'm not mistaken, space is curved and the infinity is an illusion. Travel long enough in what you fancy to be a straight line, and you'll eventually end up back where you started. Still ... I simply don't care enough to make that the hill I'm going to die on.

My life has a beginning, a middle, and an end. That's finitude enough for me.
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#33

Remove the Mysticism from Mathematics!
While I'm thinking about it, I can recommend a couple good maths channels on YouTube.  There's also Numberphile, from the same people who do Periodic Videos (also highly recommended) and Stand-up Maths, with mathematician and standup comedian Matt Parker (what he does with Excel spreadsheets is Just Not Right (™, pat. pend.)).

When you're ready for the really brainmelty stuff, there's this series of lectures on Douglas Hofstadter's Gödel Escher Bach...
"Aliens?  Us?  Is this one of your Earth jokes?"  -- Kro-Bar, The Lost Skeleton of Cadavra
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#34

Remove the Mysticism from Mathematics!
(02-24-2021, 05:34 PM)Extreme Finitism Wrote: As a computer programmer for many years, I have contemplated how a machine might 'conceive of infinitely many numbers' and I've concluded that whereas it might display the words "I can conceive of infinity" this would just be words. Everything has to be finite and so any claim of being able to experience or conceive or otherwise perceive of infinity is just a bug in the internal logic. Essentially I think that anyone who believes they can work with infinite objects (such as so-called real numbers) are deluding themselves.

When we simply count numbers there are things we cannot know. We cannot know that the numbers would continue infinitely. Nor can we know that they could continue eternally.

But reason allows us to conclude that they could. This denotes a reasoned and reasonable possibility that we cannot dismiss.

Therefore in situations like that it may not be a matter of knowledge based upon empirical evidence, but upon acceptance of the limitations of the human experience.
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#35

Remove the Mysticism from Mathematics!
(02-26-2021, 01:53 AM)trdsf Wrote: Yeah, I don't remember hearing anything about a random YouTuber winning the Fields Medal for upending all of 20th century mathematics.  I think we've got a plain old garden variety crank, of the order of someone who thinks you can make Relativity consistent with Quantum Mechanics by tacking ±ħ onto E=mc2.

Did you borrow that ħ from Kro-Bar?  Tongue

Maybe this guy is Time Cube's son?
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#36

Remove the Mysticism from Mathematics!
Time Cube? Wasn't he a member of NWA at one time?
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#37

Remove the Mysticism from Mathematics!
Had to go look up NWA. I have no idea about any connection.
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#38

Remove the Mysticism from Mathematics!
(02-26-2021, 02:46 PM)Fireball Wrote: Had to go look up NWA. I have no idea about any connection.

Ice Cube was a member of NWA. It's a joke.
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#39

Remove the Mysticism from Mathematics!
(02-26-2021, 03:24 PM)Dānu Wrote:
(02-26-2021, 02:46 PM)Fireball Wrote: Had to go look up NWA. I have no idea about any connection.

Ice Cube was a member of NWA.  It's a joke.

Who is Ice Cube?

walking-stick
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#40

Remove the Mysticism from Mathematics!
(02-26-2021, 07:26 PM)Fireball Wrote:
(02-26-2021, 03:24 PM)Dānu Wrote:
(02-26-2021, 02:46 PM)Fireball Wrote: Had to go look up NWA. I have no idea about any connection.

Ice Cube was a member of NWA.  It's a joke.

Who is Ice Cube?

walking-stick

Vanilla Ice's brother? Or is that Ice T?
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#41

Remove the Mysticism from Mathematics!
(02-26-2021, 08:46 PM)Free Wrote:
(02-26-2021, 07:26 PM)Fireball Wrote:
(02-26-2021, 03:24 PM)Dānu Wrote: Ice Cube was a member of NWA.  It's a joke.

Who is Ice Cube?

walking-stick

Vanilla Ice's brother? Or is that Ice T?

I'm like John Mayall, I hate rap music with a passion like you've never seen. I don't know the players.

I have to go look around the house. We just had a small earthquake.
If you get to thinking you’re a person of some influence, try ordering somebody else’s dog around.
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#42

Remove the Mysticism from Mathematics!
(02-26-2021, 08:53 PM)Fireball Wrote:
(02-26-2021, 08:46 PM)Free Wrote:
(02-26-2021, 07:26 PM)Fireball Wrote: Who is Ice Cube?

walking-stick

Vanilla Ice's brother? Or is that Ice T?

I'm like John Mayall, I hate rap music with a passion like you've never seen. I don't know the players.

I have to go look around the house. We just had a small earthquake.

I don't mind some rap. Like any genre, it's got its gems and its dreck.

Hope all's well at your place.
Freedom isn't free.
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#43

Remove the Mysticism from Mathematics!
(02-26-2021, 10:28 PM)Thumpalumpacus Wrote:
(02-26-2021, 08:53 PM)Fireball Wrote:
(02-26-2021, 08:46 PM)Free Wrote: Vanilla Ice's brother? Or is that Ice T?

I'm like John Mayall, I hate rap music with a passion like you've never seen. I don't know the players.

I have to go look around the house. We just had a small earthquake.

I don't mind some rap. Like any genre, it's got its gems and its dreck.

Hope all's well at your place.

I admit that I saw some act on the Cosby Show decades ago, and they pretty good, actually.

Nothing even fell over, thanks. It was centered a few miles from me. I knew it was close because the p and s waves were only a fraction of a second apart. 3.2, just a shrug.
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#44

Remove the Mysticism from Mathematics!
(02-26-2021, 11:05 PM)Fireball Wrote: I admit that I saw some act on the Cosby Show decades ago, and they pretty good, actually.

When I saw rap performed by a band, as opposed to "two turntables and a microphone", I was really impressed. There's a lot of magic in seven or eight mofos building a tight-ass groove.
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#45

Remove the Mysticism from Mathematics!
Example:



Compare to the recorded version:



The band makes the difference to me.
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#46

Remove the Mysticism from Mathematics!
I came to the party too late, sadly. All the cocktail shrimp are gone. But I'll add that metaphysics is merely a division of philosophy that is concerned with the fundamental nature of reality. And I'm not the philosopher type. I kind of stop with Kant. Reality is what makes sense.

Go at that, LOL...
Atheist born and when I die, still an atheist... Being of sound mind and body now, I intend and expect to to die an atheist.
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#47

Remove the Mysticism from Mathematics!
(02-27-2021, 02:02 AM)Thumpalumpacus Wrote: Example:



Compare to the recorded version:



The band makes the difference to me.

I have to say that in both videos, the only thing I like is that leather hat the singer was wearing in the first one. That thing was very cool! I made it less than a minute in on both. Sorry.

Not rap, but a really cool tune from the '70s. This guy never got the recognition he deserved. Check out "Purple", as well. When he sings, I'm not as enthused, though. Beautiful music!

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#48

Remove the Mysticism from Mathematics!
(02-24-2021, 03:17 PM)Extreme Finitism Wrote: If you don't believe in anything supernatural then you can say that you reject metaphysics. Metaphysics is the top-level category beneath which you'll find Religion, Mysticism, Astrology, and so on. The word 'metaphysics' literally means over and beyond physics, and so a metaphysical belief is a belief in something that is supposedly beyond physical reality.
 
In religious education classes (of enlightened countries) children are allowed to decide for themselves whether or not to accept metaphysical beliefs. Sadly the same can't be said for mathematics. In mathematics all children are indoctrinated into believing that numbers are metaphysical in nature. Most of us are not even aware that we have been duped into accepting metaphysical beliefs because we simply don't associate mathematics with mysticism. But the acceptance of non-physical objects is at the very core of this subject.

Perhaps we should try to explain numbers in terms of real-world physics. For example, when we think of a number, we might claim we form a symbol or image in our brain that is accessed by a thought process. So we might conclude that a number occurs when an algorithm uses a symbol/image as a quantity. This is arguably akin to a computer process accessing a memory location where the value in that location is treated as a numeric quantity.
 
If numbers are simply 'data currently being used as a quantity by an algorithm' then there can only ever be a finite amount of them. But for over two thousand years we have been teaching our children that numbers are intangible abstract things that are not constrained by physical reality. With this metaphysical description in place, we can then blow their minds with all sorts of weird stuff that arises due to there supposedly being infinitely many of these out-of-this-world objects.
 
Children are not given the option to believe that the brain is just physical material and has no metaphysical abilities, such as the power to conceive of abstract non physical objects of which there are supposedly infinitely many. Surely it is hypocritical for someone to claim they reject all supernatural beliefs when they accept the metaphysical foundations of mathematics, isn’t it?

Your definition of metaphysics is incorrect if it includes mathematics.
Mathematics is a language, a tool, for understanding the universe.
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#49

Remove the Mysticism from Mathematics!
(02-25-2021, 08:44 PM)Thumpalumpacus Wrote:
(02-25-2021, 07:49 PM)Extreme Finitism Wrote:
(02-25-2021, 07:30 PM)Thumpalumpacus Wrote: Once one understands mathematics as a conceptual framework to help organize human thinking about observed phenomena, any appeal to the metaphysical is moot anyway. Mathematics is simply one language of many that allows us humans to discuss observations in shared terms.

In that sense it's not metaphysical. I can draw a right-triangle and, using a tape-measure, quantify the Pythagorean theorem. Does that mean the Pythagorean theorem is metaphysical? No. It means that the Pythagorean theorem is a useful way to define some triangles we humans observe.


I agree that it began as an attempt to help organize human thinking about observed phenomena, but as Zeno and Democritus pointed out, our thinking might not always make sense in the real world. If someone travels from position A to position B and then they travel further, would it be correct to say they made the journey from A to half-way to B, then half the remaining distance to B, then half the remaining distance to B, and so on? Would it be correct to say they completed an infinite amount of journeys and then went beyond infinity to continue their journey?

If actual infinities can be completed in the real world then this is not a metaphysical position. But if there is no such thing as 'infinity' in the real world then it is a metaphysical position. Given that nobody has yet proven that an actually infinity exists or can be completed I consider it to be metaphysical until proven otherwise (in the same way that the existence of God has not yet been proven).

Also you can't draw a mathematical triangle as it would have infinitely divisible edges that were perfectly straight. Everything in the real world is granular in that it consists of a finite number of smallest parts. We've known this for over 2,000 years if we take on board the findings of Democritus and the Atomists. You can try to construct a unit square with a million smallest parts (so we define each smallest part to be one millionth of the length we define to be one unit) but you will never be able to construct a diagonal that fits perfectly.

So the Ancient Greeks could have concluded that the diagonal of a unit square cannot be constructed, and that any attempt to construct a triangle with a side of an irrational length is doomed to failure. But they went along with Plato's idea that perfect forms can be imagined and so we'll allow them. I believe this was the wrong choice. They could have said that the algorithm called 'the square root of 2' can be used to determine what length could be achieved in this case given a known 'smallest part' of length, but they chose the more 'beautiful' and 'elegant' option of accepting infinite divisibility and perfect lengths.

Well, if you keep moving you get there sooner or later, so I'm not really enamored of the infinitely-divisible halving of distances. By that logic, I can't drive to the store, because I never get there theoretically; but the fact is that I get there. Having said that, mathematics helps me get there all the same, whether we're talking about computing distance by tire revolutions, or fuel-air mixtures in the cylinders, or what-have-you.

You realize that the computer you're typing on uses mathematics in order to post online, right? It allows satellites to relay your internet connections, processes your entries to and from numbers into English, and so on. We have used mathematics to send spaceships into orbital vectors around other planets.

The fact that a process is conceptual doesn't mean that it isn't useful in reality. Mathematics need not be material in order to be useful. And there's certainly no need to appeal to metaphysics in order to justify mathematics -- as innumerable real-world processes demonstrate, mathematical conceptualization has proven its utility.

What if no intelligent life in the Universe had evolved at all? Would gravity not operate on the inverse-square function anyway?

Math is simply a human way of organizing observations of the natural world. It doesn't imply or require any superstition for it to work.

And this means its useful when used as a guide to facilitate our understanding the natural world rather than as a prescription of what that world ought to be.  It's a tool not immune to being misused.
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#50

Remove the Mysticism from Mathematics!
(02-27-2021, 06:36 PM)tomilay Wrote: And this means its useful when used as a guide to facilitate our understanding the natural world rather than as a prescription of what that world ought to be.  It's a tool not immune to being misused.

That inability to distinguish between the prescriptive and the descriptive is not unique to math.
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