OT: 0.999... = 1

I understand what you are getting at. I agree, that for almost all logical understanding, a repeating .999 pattern is 1.

An odd term I frequently encounter is Business Intelligence. Does that mean the rest of the business colleagues are stupid? I simply don’t like this type of terminology.

Try Zenos paradox

en.wikipedia.org

It’s been more years that I care to count since I took my first Calculus class, but isn’t the Fundamental Theorem of Calculus based upon infinitesimal quantities? Which once certain assumptions were made, perhaps the most important concept in modern mathematics was invented

For my money, Euler's Identity is pretty mind bendy.... en.m.wikipedia.org

I’ll just copy pasta an old joke related to the subject, which I think fits TUSCL 😁

A mathematician and an engineer agree to a psychological experiment.

The mathematician is put in a chair in a large empty room and a beautiful naked woman is placed on a bed at the other end of the room.

The psychologist explains, "You are to remain in your chair. Every five minutes, I will move your chair to a position halfway between its current location and the woman on the bed." The mathematician looks at the psychologist in disgust. "What? I'm not going to go through this. You know I'll never reach the bed!" And he gets up and storms out. The psychologist makes a note on his clipboard and ushers the engineer in.

He explains the situation, and the engineer's eyes light up and he starts drooling. The psychologist is a bit confused. "Don't you realize that you'll never reach her?"

The engineer smiles and replied, "Of course! But in less than half an hour, I'll be close enough for all practical purposes!"

If I ever get a dance from Nina, gonna tell her I wish I were her first derivative, so I could be tangent to her curves.

It's not 1. If something costs 99 cents vs a dollar. That's a huge markup and increases profits over time.

Or would you like yo own your car or just 99% of it?

Icee - I didn't say 0.99, I said 0.999...

What is 1/3 + 1/3 + 1/3? The answer is, 3/3, or 1.

1/3 is also 0.333... what is 0.333 + 0.333 + 0.333? 0.999... which is equal to 1.

Pi= 3.14____ and the number in decimal format never ends just like traveling around in circles, hence its application for circumference measurements. Pi also equals never ending search for the perfect woman, but I digress.

The square root of 69 is 8 sum, if that helps.

Motorhead, you lost me at "calculus" lol... I failed college algebra twice. 🤷‍♀️

The more accurate way of saying it is that the limit of the sum of the sequence that starts with 0.9, and where the value of subsequent numbers in the sequence is one tenth of the previous one, is 1 as the length of the sequence goes to infinity.

There are actually two kinds of infinity. The counting numbers (1, 2, ..) are countably infinite, and all the pairs of counting numbers are countably infinite. But the fractional numbers between 0 and 1 are uncountably infinite. In some sense, there are more numbers between 0 and 1 than from whole numbers from 1 to infinity.

“Mathematics is the most beautiful and most powerful creation of the human spirit.“

~ Stefan Banach ~ Born 30 March 1892 Kraków, Austria-Hungary (today Poland) ~ Died 31 August 1945 Lviv, Ukrainian SSR, Soviet Union (today Ukraine)

.99999 is the same as .9 in the real world. I'm nit talking abstract shit

What the fuck would a lying asshole like you know about the real world Icee cum stain?

Icee, you are absolutely incorrect.

LMFAO Iceydodo first says $1 > 99¢, then she says 0.9999 = .9. That's next level dumbass shit.

Okay then like I said. Own 99% of your car instead of 100%.

"Okay then like I said. Own 99% of your car instead of 100%."

".99999 is the same as .9 in the real world. I'm nit talking abstract shit"

^^^Two statements by the same dumbass...in complete contradict with one another. 🤭🤡😂😂😂

contradiction

1/3 != .333...
1/3 ~ .333...

Or in English, one third does not equal point three repeating. It's approximately point three repeating. What you're citing as a proof that .999... = 1 is an example of a rounding error, or maybe an accumulated rounding error. Ask Ed Lorenz about that.

".99999 is the same as .9 in the real world. I'm nit talking abstract shit"

^^^ Ok, like you said, own 90% of your car instead of 99.999% of it. Same thing, right dumbass? 🤯🤭🤡😂😂😂

".99999 is the same as .9 in the real world. I'm nit talking abstract shit"

i had to log off and see if that 'tard did indeed type what he typed above.

you stupid fuck!!!!! abstract is a word that pertains to art. in the real world that we live in mathematics is not fucking art!!!!

@NinaBambina

You didn’t failed college algebra twice; the education system failed, because it didn’t do what is supposed to do for you.

The United States has allowed schools to have an unequal distribution of academic resources.

Some of my students, grew up on free and reduced lunch, and some were even homeless sometimes.

It makes all the difference in the world if you are wealthy or poor, hungry students with a lot of socioeconomic problems are setup to “fail”.

The undeniable reality is that “the have and have nots”, determines student success many times.

anybody remember how richard pryor scammed all of that money in superman III?

^ or from Office Space: youtube.com

I remover they caught him when drove his Ferrari to work

Nina continues to demonstrate she is stupendously stupid. Her failing at everything she has ever attempted should surprise noone, least of all herself.

0.999... is NOT mathematically the same as one. If you calculate anything using 0.999.. you will arrive at a different solution than if you calculated with 1.

For most PRACTICAL (not mathematical) purposes, they are close enough. Fucking idiot.

Ok gammanu. Prove to me that I am incorrect in saying 0.999... = 1. You sling your insults out with such confidence that I'd like to see you mathematically back it up (just as a heads up, you won't be able to).

2 * 1= 2 2*.999... ≠ 2

There you go. Pick any number and any calculation, swap out 1 for 0.999... and you will get two different solutions.

I am always right 99.999...% of the time.

@Nina the problem with proving it is, you first have to prove that 0.999... is even a number. You have to assume it's a number to multiply it by 10.

One of my favs is studying to be a nurse, and they've told her she has to take a Calculus class. That is so profoundly fucked up. Seems very unlikely a nurse would need anything more than very basic Algebra.

For 0.999 to be equal you have to type it in the calculator as 0.99999999 like ten 9s. And its not actually 1 it’s just close enough to one. 0.9999 is 99.99%, so clearly different from 1 or 100%. 99.99999999% in most scenarios will come out close to 100%.

1/3 is not 0.333, in a calculator it will show as 0.333333333 and in most scenarios that’s close enough. Actually the calculator is treating it as an infinite 0.33333333.

Gammanu, incorrect.

0.999... (again, ellipsis meaning infitie 9s) × 2 is 2.

Go on a calculator and type 0.999999999999999999999999999999 × 2 and come back with your answer.

Infinite*

0.999... × 2 is 2.

My gut feeling here is that much of this disagreeing with Nina has more to do with being disagreeable than being correct. Because you don't have to search very hard to discover that what she posted is mathematically valid.

^Yup! 😊

Maybe Nina would not have failed if she were not relying in her pink HelloKitty make in Malaysia calculator to do her formulas.

1.9999999999999999999999999999999999998≠2

Naw, she'd still fail.

It reminds me of a problem that we faced when I was an engineering manager. One of the guys who worked for me had made a very elegant algorithm for anchor chain catenary to in turn calculate the stress in the chain. The problem was that his algorithm kept blowing up on one machine while working on the other (IBM PS2 Model 30s) and it was driving him crazy. I thought about for a few minutes and thought, "Hmmm. The machine it doesn't work on has a math coprocessor, and the one it works on doesn't...

As it turned out, the increased precision of the coprocessor allowed the tangent function to blow up out of range. A simple step to define the expected result at an angle of more than 89.9 degrees solved the problem.

Rebuttal link: sciforums.com

I can agree that it is paradoxical.

I tried to pay a stripper $19.9999999999… for a $20 dance -

I explained it to her - and I explained it to the bouncer right before he tossed me out of the club where I landed and broke off approximately.9999… of my front tooth.

So, it didn’t work well with the dancer or bouncer, but I effectively lost a full tooth.

"gammanu95, I think you should read the wiki page I referred to earlier."

He won't. He would rather stay ignorant on the subject than condescend to admit that I was right.

Boobs

This thread is one of the dumbest here. In the real world its called skimming.

"Boobs" Longball300, show your calculations.

ih1.redbubble.net

"This thread is one of the dumbest here."

^^^ it's coz there are dumbasses that don't know math that post as if they do. Like the dumbass that posted .99999 = .9 🤭🤡😂😂😂

Result of my calculation:

tuscl.net

...birds are dinosaurs.

Soylent Green is People

Sorry Nina but we all know - birds aren’t real!

birdsarentreal.com

When dealing with women you always have to invoke Satan. Feel ups and DATY so so. But for DFKing and entry, it is always Satan who finally does it.

SJG

Oh, great, the antichrist.

.999 upside down is 666. Just sayin'.

^ That's how to respond to having a naked woman across the room from you. It gets real simple.

SJG

School of Rock AllStars perform "Highway Star" by Deep Purple youtube.com

".999 upside down is 666. Just sayin'."

are you trying to intertwine this thread with the satanic one?

You need Satan in situations like that, presented with a naked woman across the room, but you will never be able to get there.

Satan changes the rules.

SJG

School of Rock AllStars perform "Highway Star" by Deep Purple youtube.com

"are you trying to intertwine this thread with the satanic one?"

Naw. Just giving a possible theory as to why san_jose_creep is, though.

Satan is very important. We would all be lost without him.

SJG

The Heisenberg Uncertainty Principle. One form of this is: you can't know both the speed and position of a quantum particle, at the same time. The more precise you measure one, the more uncertain the other becomes.

It's easy to think of this as just a limitation on what we can measure. Like, if you measure the position of an electron, with high precision, the measurement itself changes the speed. But that's the wrong way to think about it. The HUP is in fact a statement about the fundamental nature of the universe. If you measure an electron's speed with infinitely high precision, then its location becomes infinitely variable -- it can, in fact, be anywhere in the universe at the point its speed is measured, though it does follow a probability function.

This principle is so fundamental that it can be put to use by engineers. There are transistors, like the ones powering the chips in your phone, which rely on a principle called quantum tunneling, which is HUP applied to energy states: electrons can simply disappear from one side of a barrier that is "uncrossable", and simply re-appear on the other side. This is engineered into certain types of transistors, and those transistors rely on electrons doing this, in order to function.

... and I'll add, in many computer chips, they do NOT want quantum tunneling to happen. Since it happens anyway (since an electron's position is merely a probability and not a physical fact anyway), various techniques are used to STOP electronics from quantum tunneling all around the chip.

^ all very true.

Quantum tunneling is the key to Floating Gate Mosfets, the kind of read / write chips which can store data power-off.

Some might see Satan as operating in this region of uncertainty.

We need Satan because he can take the reigns and show us what to do when presented with a naked woman across the room.

SJG

Red Hot Chili Peppers youtube.com

This discussion took an unexpected turn!

I feel sophomoric for posting a comment about birds not being real - with all this devil stuff.

m.youtube.com

Tunneling is a way for electrons to get through a hard insulator without enough of a potential difference to be able to cross. By classical mechanics they would never be able to cross. But with HUP, they have some chance of crossing, and this is what makes for nice non-volatile memories, and we need this for modern digital devices. Can't use the old fuse blow types.

Unwanted tunneling, I would say that it is not a problem when a node is not supposed to be insulated. A little bit of tunneling just sinks back to ground.

With floating gates though, unwanted tunneling will compromise the memory.

SJG

Red Hot Chili Peppers - By The Way youtube.com

The issue with quantum tunnelling is simply that the overall size of the transistor and conductors on a chip are approaching the size of atoms themselves, where quantum physics/chemistry matter. And their relative placement from one another are small dimensions too. Everything is literally getting smaller on a chip. As such, the quantum physics is coming more into play than the classical physics.

A transistor on a chip is down to less than 10 nanometers in size. The conductor sizes are also on this order of magnitude in size. Copper or gold "wires" on a chip are literally only several atoms in diameter. Also everything is placed in close proximity to each other. Again, these are all size scales where quantum physics/chemistry matter more.

The Cross Seamount Beaked Whale is a species we've known about for many years now, but has only been classified via acoustic vocalizations. Despite many attempts over the years, it has never been visually identified. It's a large marine mammal species that is active around Hawaii, but no one has ever seen it.

Not quite getting down to the size of atoms, but getting very small and quantum mechanics does matter. But quantum mechanics has been how we predicted the band structure by which we are able to use semiconductors.

Shockley, William, 1910-1989.

Electrons and holes in semiconductors, with applications to transistor electronics [1950]

Mostly based on work done before the war, and before their 1947 Nobel Prize winning work.

Tunneling is about uncertainty which is at the bottom of quantum mechanics, and this is how electrons are able to get beyond potential barriers in a way which classical mechanics would not allow for.

Speaking to the OP and to Nicespice's example, and to Subraman's response, the Uncertainty Principle can be evoked to explain the inexplicable. And you can relate this to the occult.

Chaos Magick Pioneer Peter J. Carroll has tried to develop this into a formal theory.

amazon.com

And he is trying to follow James Gleick amazon.com

But the problem is that while yes there is a new kind of science built around Chaos Theory, or more formally Dynamic Systems Theory, this has nothing to do with the Heisenberg Uncertainty Principle.

Dynamic systems will display chaotic behavior, but they are still entirely deterministic. It is not due to noise, or round-off error, and it is not due to HUP. It is simply that you have high degrees of non-linearity and that it is impossible to ever have enough accuracy in the initial conditions.

In an earlier era there was also interest in trying to explain phenomenon of parapsychology via Heisenberg. These people, known as the Berkeley Fundamental Physics Group.

amazon.com

One of the things they took interest in was Quantum Entanglement. And there is some real science there and there are somethings unknown about it. But much of the early interest was driven by assumptions which were just plain wrong.

SJG

Should be appreciated inch by inch, on the outside, and then millimeter by millimeter on the inside. tuscl.net tuscl.net

Kansas City School of Rock Supermassive Black Hole Muse ( I like this version much better than the original artist ) youtu.be

Whoever informed SJG that he can post photos in TUSCL threads needs kicked in the nuts, 1 time or .999999… times. Rounding up to 2 - once for each of his nuts would be okay too.

^

Agreed, kick the creep in the nuts too if he actually has any.

san_jose_creep your "understanding" of science and math is very convoluted and you often try to connect things that have very little relevance to each other. You clearly only understand from a cursory level, but not from the true and exact mathematical level. It's like you read books about all this technical stuff but you can't and don't actually perform the mathematical proofs or problems yourself. And then due to your ignorance you make false assumptions and connections that are unfounded. In other words, you only know enough about a topic to "be dangerous", and you don't truly understand it.

For example your understanding and explanation of tunnelling is not quite correct. It has more to do with probability than uncertainty and the Heisenberg Uncertainty Principle. Any small particle (like an electron) can simply exist anywhere in space, and there is a mathematical probability equation that defines this. This probability drops off significantly with the distance from a known point. And even the media in which it exists is also a variable. So as stated before, when you have transistors and conductors that approach (<-note that I said approach and not equal) the size of atoms, then there is a higher probability that the electrons in the transistor or conductor can "tunnel" to another location which is outside of where it is supposed to be. This is why it is problematic with today's chips - their literal dimensions are now so small that quantum physics is significant. When chips were literally bigger several years ago, the quantum physics mattered less.

It is not just via approaching the size of atoms. It is also the momentum.

de Broglie Postulate

chem.libretexts.org

Proportionality of wavelength to inverse of momentum via the Heisenberg constant.

The Heisenberg principle arises from wave particle duality. Sometimes particles will be seen to be acting as particles, and other times they will be seen to be acting as waves. And it is in this latter situation that this uncertainty comes into play. And then this is when this "tunneling" can manifest. Not just a function of size, but also of momentum, which is closely related to energy.

And yes, this is getting more important today. But it is in these Floating Gate MOS devices that they first sought to deliberately use this tunneling. But it is for quantum mechanical reasons that we even have semiconductor band structure.

SJG

Should be appreciated inch by inch, on the outside, and then millimeter by millimeter on the inside. tuscl.net tuscl.net

Kansas City School of Rock Supermassive Black Hole Muse ( I like this version much better than the original artist ) youtu.be

^^^again you are convoluting things. And it's not worth unpacking for you.

Go back to school and really learn how to do and understand the math of what you are currently just regurgitating from reading books about it in the library.

Quantum mechanics has always been a huge factor in solid state physics, going back to the 1920s. It is now that semiconductor dimensions and momentums are getting small enough and large enough to matter in the devices, not just in the crystalline solids. But it was in these Floating Gate non-volatile memory devices that tunneling was first deliberately used. And it does depend on the uncertainty principle, which has also been of interest to occultists, and I think that suggestion of my mention of Satan in relation to Nicespice's example is what Subraman was getting at.

SJG

Should be appreciated inch by inch, on the outside, and then millimeter by millimeter on the inside. tuscl.net tuscl.net

Kansas City School of Rock Supermassive Black Hole Muse ( I like this version much better than the original artist ) youtu.be

"And it does depend on the uncertainty principle"

^^^I never said it didn't. I just said that it had MORE to to with probability than uncertainty.

And I understand the Heisenberg Uncertainty Principle, deBroglie wavelengths, and everything alse you are rambling about well. I've actually had to do math problems and calculations based on it all.

As stated, go back to school and really learn how to do and understand the math of what you are currently just regurgitating from reading books about it in the library.

I thought the point of this thread was to identify interesting mathematical phenomena. For example, anyone in finance or banking, or who's ever taken the Series 7 exam, probably knows about the "Rule of 72". This is a simple calculation that determines how long an investment will take to double its value at a consistent rate of return.

For example: If you could invest in something (let's say a CD to keep it simple) at 3% interest, you divide the number 72 by 3, which means it will take 24 years to double your money. If you found a 10% investment, it would only take 7.2 years to double.

Conversely, if you were to borrow money (say, on a credit card) at 12% interest, your debt would double in 6 years (assuming you paid nothing on the debt). 72/12=6

How or why this works I'm sure I have no idea. But it's a fact.

sirlap-you get major props from me. i just looked up examples of sample equations pertaining to debroglie wavelengths. lots of scientific notation being used. a hard core introduction to advanced physics. i sir salute you!!!

Uncertainty is how you take something which in classical mechanics would be deterministic, and turn it into probability.

And this probability is how you get electron tunneling in situations where classical mechanics would say they could not cross a potential barrier.

And some look to this as the explanation for occult and para psychology phenomenon, which I think is what Subraman was getting at in replying to my introduction of Satan in response to Nicespice's examples.

SJG

Should be appreciated inch by inch, on the outside, and then millimeter by millimeter on the inside. tuscl.net tuscl.net

Kansas City School of Rock Supermassive Black Hole Muse ( I like this version much better than the original artist ) youtu.be

School of Rock Communications Breakdown youtube.com

@rattdog I appreciate the comments. At my school (UC Berkeley) my best subject was quantum chemistry. It was the only class where I got an A+. And yeah, the math is pretty hard. In short it's the combination of probability distributions, calculus, and, at times, imaginary numbers all jumbled together.

And just to add to the thread topic I'll say that vector calculus and differential equations were the most difficult math topics that I've ever faced. The mindfuck to me was that it's calculus in three dimensions. Instead of just 'x' as the calculus variable, with vector calculus you have to also solve for'y' and 'z' at the same time you solve for 'x'. 🤯🤯🤯

"Uncertainty is how you take something which in classical mechanics would be deterministic, and turn it into probability."

^^^As stated @san_jose_creep, go back to school and really learn how to do and understand the math of what you are currently just regurgitating from reading books about it in the library.

Uncertainty is related to a particle's probability wave function, but it is NOT the basis of it. Once again, your understanding of this is convoluted.

I went through high school thinking that taking the square root of a negative number was truly 'imaginary' and completely useless from a scientific standpoint. And then I get to college and it comes back to me in the math of quantum chemistry and wave functions. That was another math mindfuck to me. 🤯

i is used heavily in engineering too to indicate phase. Years ago so I barely remember Fourier transforms etc but fun fun!

I say this in a good way but what a bunch of F'ng nerds. I studied that stuff but don't need to use it to work on networks. That stuff just provided a background that was needed to do real life application of electronics.

heaving you sound like an EE or physicist talking Fourier transforms and CMOS devices. Also a process engineer.

"I'm EE PhD."

@heaving I'm not surprised and have much respect for you. Getting to that level takes an excellent mathematician AND mastery of all the pure sciences. 👏👏👏👍👍

And now he's here mastering the impure sciences!

My mind is still fucked when I think about how computer chips do what they do. At its core, a chip transistor is producing a 1 or 0 result. Or you can think of it as a yes or no answer. And through thousands and thousands of transistors basically answering in this yes/no fashion, we get the ability to post on TUSCL or watch a CGI movie. It's simple binary logic doing advanced analog things in real life. Never ceases to blow my mind.

For those who were arguing about the original question, whether 0.999.. (repeating) equals 1, here's another proof.

Let x = 0.99999999... (repeating). Then 10x = 9.99999999.... (repeating) because multiplying by 10 moves the decimal one place to the left. Take the difference and simplify 10x - x = 9.9999999... - 0.999999... 9*x = 9.0 x = 1.0 Thus demonstrating that 0.99999 (repeating) is exactly equal to one. Yes, subtracting the two repeating decimal numbers given an integer value. All of the digits are the same so they cancel exactly.

Any field that tries to make things more difficult to understand is questionable. Thats why many people hate "mathematicians." How about trying to make things more understandable instead of more esoteric?

And some of you wonder why you have to go to strip clubs to meet women? Just kidding. Well maybe.

^ I'd like to introduce everyone to the Olympic Gold Medal Winner in the "Throwing Stones in a Glass House" competition.

Fuck off poopey breath

^ Truth hurts.

I've won a few bar bet with Abbott & Costello math, proving 7*13 = 28.

youtu.be

re: nicespice psych experiment. But if you put a football on the 1 yard and get just half way closer with every play you will never score.

If I put $0.9999... into a vending machine I won't be able to get the $1 item.

@yahtzee74: Of course you'd score. First down from the 1. Second from the 1/2. Third from 9 inch line. Fourth down from the 4.5 inch line and the chip shot field goal is good.

If you can figure out how to put fractions of a penny into a vending machine then you can figure out how to get it to give you the item. Probably for free.

There are arguments against the claim too that you can find on the internet. Wikipedia in general sucks so I would be skeptical of any claims they make. For example their entry on this subject should at least include some of the counter theories so it makes them seem biased.

Other mindfucks:

There are galaxies currently receding from us faster than the speed of light (due to expansion of the universe), so the light from those galaxies will never reach us, and we'll never see them.

The galaxies we do see, eventually the light from them will be so far redshifted (due to the expansion of the universe) that we won't be able to see them with the naked eye. This will eventually happen with all the stars in our galaxy, and the sky will be dark.

This all assumes the universe will keep expanding at its current rate and acceleration, which is not certain.

And the physics which has current industrial applications is very different from the above, but it is still just as complex to apply.

What new applications can use higher energy levels and deal with larger masses and gravitational fields?

SJG

Subraman - also, in a few billion years the earth will be engulfed by the sun.

It's also crazy to think of how everything in the universe is able to exist and work because of meticulous little consistencies. If these were to change on a microscopic level, life would end as we know it.

Yep, everything perfectly balanced!

I am .999... percent sure Subraman and SJG will never start their organization because of the ongoing shortage of microchips.

They say that before our sun runs out, the Andromeda Galaxy will collide with our Milky Way Galaxy and everything will be torn apart. Earth and Sun could be destroyed. Maybe only 1 billion years out.

SJG

School of Rock AllStars perform "Highway Star" by Deep Purple youtube.com

"If I put $0.9999... into a vending machine I won't be able to get the $1 item."

^^^In theory you'd have to do it for infinity and then you'd get the item.

"It's also crazy to think of how everything in the universe is able to exist and work because of meticulous little consistencies. If these were to change on a microscopic level, life would end as we know it."

^^^I see it as a scale and relative issue. The universe is simply macroscopic to us/humans/humanity. We are microscopic in scale so a star expanding, to us, seems like a very long time. But to the universe it's like the blink of an eye.

I think Nina is talking about the perfect balance of forces to create the universe. If gravity were even a smidge weaker, the major bodies of the universe (stars, planets) wouldn't have formed before they got expanded away; a smidge stronger, and it would have collapsed on itself. If the nuclear strong force were the tiniest bit stronger or weaker, all atoms either fuse together or fly apart. You can go on and on and on, one coincidence after another of either perfectly set, or there is no universe

@Subra I get that too, but who's to say that us/life/humanity wouldn't have existed, albeit briefly, in a collapsing universe?

And if the expanding universe is "true", who's to say it's not on a path to oblivion?

My point is that our lives and humanity is so short, relatively speaking, that it could still exist in universes with slightly different "balances".

Nina, SirLap, and Subra, I too have always taken note of such issues, a seeming balance and interplay.

I have not read this but I have always wanted to and I think it addresses this, the issue of scale.

amazon.com

SJG

School of Rock AllStars perform "Highway Star" by Deep Purple youtube.com

Speaking of scale, when I read 'Chaos' for the first time, my mind blew when I got to the part about fractals and Mandelbrot.

youtu.be

a = b a * a = b * a a * a - b * b = b * a - b * b (a + b)(a - b) = b * (a - b) Divide both sides by a - b a + b = b But since a = b b + b = b 2 * b = b Divide both sides by b: 2 = 1

If you haven't seen this before, the error is that a - b is zero, and you can't divide by zero.

The problem with the 0.999... thing is, you can't just assume that's a number.

x = 2 + 4 + 8 + 16 + ... 2x = 4 + 8 + 16 + 32 + ... 2x - x = 2 x = 2

The difference is that x is not a convergent infinite series, but 0.999... is. But it's still mathematically more correct to say 1 is the limit of the convergent series 0.999... is 1, not that 0.999... equals 1.

I graduated in Naval Architecture and Marine Engineering. When I was studying for a business masters, I went to the dean to discuss potential prerequisites and/or exemptions. He allowed that my undergrad macro economics course could exempt me from microeconomics 101.

I signed up for the economics course and the professor was unimpressed and predicted a dismal outcome for me. "After all, there is a lot of calculus in this course," he said.

I laughed in his face and replied, "Sir, I have passed vector calculus with an A. You don't have any math that can scare me!"😂

People need to practice mathematics daily to stay current.

SJG

Quantum Mechanics:

20 page pdf scholar.harvard.edu

" In quantum mechanics, particles have wavelike properties, and a particular wave equation, the Schrodinger equation, governs how these waves behave. "

" 1900 (Planck): Max Planck proposed that light with frequency ν is emitted in quantized lumps of energy that come in integral multiples of the quantity, "

" The energy is therefore essentially continuous for most purposes. However, a puzzle in late 19th-century physics was the blackbody radiation problem. In a nutshell, the issue was that the classical (continuous) theory of light predicted that certain objects would radiate an infinite amount of energy, which of course can’t be correct. Planck’s hypothesis of quantized radiation not only got rid of the problem of the infinity, but also correctly predicted the shape of the power curve as a function of temperature. "

"1924 (de Broglie): Louis de Broglie proposed that all particles are associated with waves, where the frequency and wavenumber of the wave are given by the same relations we found above for photons, namely E = ¯hω and p = ¯hk. The larger E and p are, the larger ω and k are. Even for small E and p that are typical of a photon, ω and k are very large because ¯h is so small. So any everyday-sized particle with large (in comparison) energy and momentum values will have extremely large ω and k values. This (among other reasons) makes it virtually impossible to observe the wave nature of macroscopic amounts of matter. This proposal (that E = ¯hω and p = ¯hk also hold for massive particles) was a big step, because many things that are true for photons are not true for massive (and nonrelativistic) particles. For example, E = pc (and hence ω = ck) holds only for massless particles (we’ll see below how ω and k are related for massive particles). But the proposal was a reasonable one to try. And it turned out to be correct, in view of the fact that the resulting predictions agree with experiments. The fact that any particle has a wave associated with it leads to the so-called waveparticle duality. Are things particles, or waves, or both? Well, it depends what you’re doing with them. Sometimes things behave like waves, sometimes they behave like particles. A vaguely true statement is that things behave like waves until a measurement takes place, at which point they behave like particles. However, approximately one million things are left unaddressed in that sentence. The wave-particle duality is one of the things that few people, if any, understand about quantum mechanics. "

" 1925 (Heisenberg): Werner Heisenberg formulated a version of quantum mechanics that made use of matrix mechanics. We won’t deal with this matrix formulation (it’s rather difficult), but instead with the following wave formulation due to Schrodinger (this is a waves book, after all). "

" 1926 (Schrodinger): Erwin Schrodinger formulated a version of quantum mechanics that was based on waves. He wrote down a wave equation (the so-called Schrodinger equation) that governs how the waves evolve in space and time. We’ll deal with this equation in depth below. Even though the equation is correct, the correct interpretation of what the wave actually meant was still missing. Initially Schrodinger thought (incorrectly) that the wave represented the charge density. "

" 1926 (Born): Max Born correctly interpreted Schrodinger’s wave as a probability amplitude. By “amplitude” we mean that the wave must be squared to obtain the desired probability. More precisely, since the wave (as we’ll see) is in general complex, we need to square its absolute value. This yields the probability of finding a particle at a given location (assuming that the wave is written as a function of x). This probability isn’t a consequence of ignorance, as is the case with virtually every other example of probability you’re familiar with. For example, in a coin toss, if you know everything about the initial motion of the coin (velocity, angular velocity), along with all external influences (air currents, nature of the floor it lands on, etc.), then you can predict which side will land facing up. Quantum mechanical probabilities aren’t like this. They aren’t a consequence of missing information. The probabilities are truly random, and there is no further information (so-called “hidden variables”) that will make things unrandom. The topic of hidden variables includes various theorems (such as Bell’s theorem) and experimental results that you will learn about in a quantum mechanics course. "

" 1926 (Dirac): Paul Dirac showed that Heisenberg’s and Schrodinger’s versions of quantum mechanics were equivalent, in that they could both be derived from a more general version of quantum mechanics "

Introduction to classical mechanics : with problems and solutions / David Morin (2019, written a few books)

SJG

etsy.com

Quantum tunneling in low-dimensional semiconductors mediated by virtual photons

Quantum tunneling, a phenomenon that has no counterpart in classical physics, is the quantum-mechanical process by which a microscopic particle can transition through a potential barrier even when the energy of the incident particle is lower than the height of the potential barrier. In this work, a mechanism based on electron/hole annihilation and creation with the participation of virtual photons is proposed as an alternative to explain quantum tunneling processes in semiconductors. Finally, tunneling times are discussed within the proposed framework.

aip.scitation.org

In classical mechanics, a particle with energy E, which encounters a potential barrier V0 on its path will reflect from it if V0 > E. However, the quantum-mechanical description allows for the particle to be transmitted through the potential barrier. Nevertheless, in addition to being a counterintuitive phenomenon, justifying that tunneling occurs even if the energy of the incoming particle is smaller than that of the barrier has traditionally posed a philosophical puzzle.

Quantum tunneling can be considered a consequence of describing the physical state of a particle using the Schrödinger equation since the wavefunction is not required to be zero inside the barrier. Accordingly, there is a probability different from zero to find the particle into the classically forbidden region. Different methods are commonly employed to calculate the transmission (or reflection) probability, the WKB approximation being the most widely used.3

[now this is going beyond my understanding] FIG. 1. Feynman diagram for the lowest-order term of the proposed mechanism for quantum tunneling through a potential barrier. At this order, the only possible intermediate state is a photon (γ).

R. J. Martín-Palma and J. M. Martínez-Duart, Nanotechnology for Microelectronics and Photonics, 2nd ed. (Elsevier, 2017).

D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Prentice-Hall, Upper Saddle River, 2005).

P. Harrison and A. Valavanis, Quantum Wells, Wires, and Dots, 4th ed. (John Wiley & Sons, Chichester, 2016)

SJG

etsy.com

Most people know about Fritjof Capra's Tao of Physics.

The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism

amazon.com

There is another book kind of similar of interest to me, Heinz Pagels:

The cosmic code : quantum physics as the language of nature / Heinz R. Pagels. (1982)

amazon.com

preview amazon.com

**

I've always known Pagel's name. But he died very young in a tragic accident. I read the book his widow wrote chronicling all of this.

SJG

I bet Nina didn't expect that she'd get new post notifications emailed to her for the rest of her life (well, for the rest of SJG's life...) because he's too obnoxious and narcissistic to start his own thread on this.

Cim doesn't really mean that. He only posts to be an obnoxious troll

CMI, head filled with Styrofoam, after they removed his brain and put him in a take with bags of Epsom salts dissolved in water. They don't want the water getting into his empty brain case.

SJG

^ You should stop getting your weird taunts from the kids at the playground. I'm sure that there's a restraining order in place.

It also doesn't change the fact that you're hijacking someone else's thread... again.

Heinz Pagels is completely in line with the OP. LEARN TO READ YOU WORTHLESS PIECE OF SHIT!

Oh, I forgot:

Ishmael floating in a tank. That 2 inch diameter hole they they used a circle cutter to make in his forehead.

Umbilical cable runs through that hole, as he floats on his back. The cable has wires, optical fibers, and tubes. This cable runs through his empty brain case, and connects with his spinal column.

They sealed around the two inch hole with Silicone RTV, and then they injected Styrofoam into his empty brain case. A boom mounted on the ceiling holds the umbilical cable's weight so that is doesn't make Ishmael sink or capsize while floating in the Epsom Salts Solution.

SJG

Nina, if you posed that question to me in the club, I'd say: "0.999...=1 is close enough for government work, how about we adjoin to the VIP for some dances."

There are as many integers as there are rational numbers (fractions). But there are more irrational numbers than rational numbers.

^ very true, and calculus is based on this.

Some of these guys have been considered showman. But they are all involved in Quantum Information Theory, Quantum Entanglement, and Quantum Security:

nytimes.com

cnn.com

arstechnica.com

bbc.com

w/video reuters.com

npr.org

quantamagazine.org

w/video nbcnews.com

space.com

SJG

Dang, can you believe we got this thread well above a hundred posts? Whoda thunk titty-obsessed brains would have room for so much math?

S = 1 + 2 + 3 + 4 + ... S = 1 + 2 + 3 + ... Subtracting: 0 = 1 + 1 + 1 + ... But: 1 - 1 + 1 - 1 + ... = (1 + 1 + 1 + ...) - (1 + 1 + 1 + ...) = 0 - 0 = 0 Since 0 is not equal 1/2, that proves by contradiction that the original assertion, that: 1 - 1 + 1 - 1 + ... = 1/2 is false.

The moral of the story being, the brain eaten by the zombie thread you bring forth may be your own.