Daily "Check In" Thread For Us

[Mountaineer]

Good morning fellow cats and dogs. I'm still here. Here is something to lighten us up a bit:

Personal Ad: Single man w/TP seeks single woman w/hand sanitizer.

How long is this social distancing supposed to last? My husband keeps trying to get into the house.

Neil diamond is posting a video of himself singing “Sweet Caroline" with the lyrics…
”hands…washing hands…don’t touch me…I won’t touch you…"

[dualstow]

...

Neil diamond is posting a video of himself singing “Sweet Caroline" with the lyrics…
”hands…washing hands…don’t touch me…I won’t touch you…"

I've seen that. It's so great. And his voice hasn't changed!

[Smith1776]

I finished my math assignment.

I think I've developed PTSD.

[stuper1]

I finished my math assignment.

I think I've developed PTSD.

I hope this doesn't sound snide, because I don't mean it that way at all, I'm just genuinely curious.

Why does someone who doesn't like math have a beautiful math equation as his signature line?

By the way, that math equation blows my mind every time I look at it. It's quite amazing to think that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

Also, in one of your earlier posts you said that "infinite series suck". I could be wrong, but I'm pretty sure that there is no way to prove that beautiful math equation without using infinite series, so obviously they are quite useful.

[Mountaineer]

I finished my math assignment.

I think I've developed PTSD.

PTMA (post traumatic math assignment).

[Xan]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

[stuper1]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

You say the magic is really in i, but that's not so clear to me. We defined i as the square root of -1. We defined pi as the ratio of circumference to diameter. We defined e as the natural logarithm of 1. To me, it seems that we "invented" all of these things, or maybe a better word is "discovered". Then, the magic is that when they are combined in a certain way, which nobody had even thought of when the original definitions were made, instead of getting a nonsense irrational-number result like say 4.6239281394821..., we get an absolute whole number of -1.

[Mountaineer]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

You say the magic is really in i, but that's not so clear to me. We defined i as the square root of -1. We defined pi as the ratio of circumference to diameter. We defined e as the natural logarithm of 1. To me, it seems that we "invented" all of these things, or maybe a better word is "discovered". Then, the magic is that when they are combined in a certain way, which nobody had even thought of when the original definitions were made, instead of getting a nonsense irrational-number result like say 4.6239281394821..., we get an absolute whole number of -1.

pi - discovered

e - iffy (but not sure, probably discovered)

i - invented

mo - my opinion to the nth power where n = infinity

[Xan]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

You say the magic is really in i, but that's not so clear to me. We defined i as the square root of -1. We defined pi as the ratio of circumference to diameter. We defined e as the natural logarithm of 1. To me, it seems that we "invented" all of these things, or maybe a better word is "discovered". Then, the magic is that when they are combined in a certain way, which nobody had even thought of when the original definitions were made, instead of getting a nonsense irrational-number result like say 4.6239281394821..., we get an absolute whole number of -1.

e is a number, as you said, 2.71828 etc. It was discovered. pi is the ratio of circumference to diameter, 3.14159 etc, as you said. Combining those in any way to get a whole number would be totally weird. It's the square root of -1 which makes that happen. We defined its behavior completely. It isn't a number like 2.71828. I think we may have defined that e^iπ = -1 when defining how i works.

Just saw Mountaineer's post. Yes, i definitely qualifies as an invention, much more so that particular points on the number line like e and π.

[stuper1]

Hmmm, I'm not convinced. The equation we're talking about is called the Euler identity.

Mathematicians seem to think that the Euler identity is quite elegant. Why would they think that if they basically just defined it into existence?

I could take a few greek symbols and give them my own definitions that lead to a complex equation. Would that make it an elegant equation?

[Libertarian666]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

You say the magic is really in i, but that's not so clear to me. We defined i as the square root of -1. We defined pi as the ratio of circumference to diameter. We defined e as the natural logarithm of 1. To me, it seems that we "invented" all of these things, or maybe a better word is "discovered". Then, the magic is that when they are combined in a certain way, which nobody had even thought of when the original definitions were made, instead of getting a nonsense irrational-number result like say 4.6239281394821..., we get an absolute whole number of -1.

e is a number, as you said, 2.71828 etc. It was discovered. pi is the ratio of circumference to diameter, 3.14159 etc, as you said. Combining those in any way to get a whole number would be totally weird. It's the square root of -1 which makes that happen. We defined its behavior completely. It isn't a number like 2.71828. I think we may have defined that e^iπ = -1 when defining how i works.

Just saw Mountaineer's post. Yes, i definitely qualifies as an invention, much more so that particular points on the number line like e and π.

i is a point on a number line. That line just happens to be perpendicular to the "real" number line.
And I do NOT agree that Euler's identity is what defines i. It is an amazing discovery that happened after the invention (discovery) of i.

[Tortoise]

And I do NOT agree that Euler's identity is what defines i. It is an amazing discovery that happened after the invention (discovery) of i.

This.

And Euler's identity is just a special case of the more general Euler's formula (also a discovery) that relates complex exponentials to trigonometric functions:

https://en.wikipedia.org/wiki/Euler%27s_formula

[stuper1]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

That Kronecker quote kind of gets to the heart of the issue for me. According to Kronecker, God made the natural numbers, which are just the positive integers 1, 2, 3, 4, and so on. Man made the rest, which would include pi, e, and i. (Having said that, I agree that pi for sure seems like a discovered thing, not invented, but I'm trying to run with Kronecker for a bit.)

And yet we come up with all kinds of amazing combinations of these things which were never imagined when man invented them. To me at least that suggests that there is some underlying system to the whole thing. Did that system just happen by chance? Seems unlikely. Maybe Kronecker was wrong. Maybe the whole system was made by God.

[Libertarian666]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

That Kronecker quote kind of gets to the heart of the issue for me. According to Kronecker, God made the natural numbers, which are just the positive integers 1, 2, 3, 4, and so on. Man made the rest, which would include pi, e, and i. (Having said that, I agree that pi for sure seems like a discovered thing, not invented, but I'm trying to run with Kronecker for a bit.)

And yet we come up with all kinds of amazing combinations of these things which were never imagined when man invented them. To me at least that suggests that there is some underlying system to the whole thing. Did that system just happen by chance? Seems unlikely. Maybe Kronecker was wrong. Maybe the whole system was made by God.

I'm not conventionally religious but I'll go with the latter theory.

[Smith1776]

I finished my math assignment.

I think I've developed PTSD.

I hope this doesn't sound snide, because I don't mean it that way at all, I'm just genuinely curious.

Why does someone who doesn't like math have a beautiful math equation as his signature line?

By the way, that math equation blows my mind every time I look at it. It's quite amazing to think that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

Also, in one of your earlier posts you said that "infinite series suck". I could be wrong, but I'm pretty sure that there is no way to prove that beautiful math equation without using infinite series, so obviously they are quite useful.

Not snide at all! It's a totally fair question. The truth is that I actually really enjoy math. My degree is a double concentration in math and computer science. It's just that this last semester has just really been a lot for me, and I think I need at least a break from math for now.

As I mentioned in some previous posts, the required math I have to do is all done now. Everything else from here on out is optional!

[yankees60]

I finished my math assignment.

I think I've developed PTSD.

I hope this doesn't sound snide, because I don't mean it that way at all, I'm just genuinely curious.

Why does someone who doesn't like math have a beautiful math equation as his signature line?

By the way, that math equation blows my mind every time I look at it. It's quite amazing to think that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

Also, in one of your earlier posts you said that "infinite series suck". I could be wrong, but I'm pretty sure that there is no way to prove that beautiful math equation without using infinite series, so obviously they are quite useful.

Not snide at all! It's a totally fair question. The truth is that I actually really enjoy math. My degree is a double concentration in math and computer science. It's just that this last semester has just really been a lot for me, and I think I need at least a break from math for now.

As I mentioned in some previous posts, the required math I have to do is all done now. Everything else from here on out is optional!

You bring back "bad" memories!

I took calculus in high school. Took the advanced placement exam. Go the highest score - a 5 -- "Extremely well qualified".

Therefore when I entered WPI (Worcester Polytechnic Institute) I had 7 credits before I even took a class.

I told everyone that I was going to major in math and computer science. Seemed appropriate at the time.

That first year Math continued to be my strong suit - A's in Math III and Math IV. Absolutely loved that Math IV differential equations course. All numbers and formulas.

However the second semester of freshman year I had to take a computer science course that was required for all students at the school (as were these required for all: the four math courses, two semesters of chemistry, and three semesters of physics).

I just could NOT fathom the concept of bits and bytes! I got so frustrated with it all that I did a quick calculation in my head of what getting an F in the course would do to my GPA and realized it could handle an F. I then proceeded to push the book to the back of my closet saying that I'm not going to let this unfathomable (to me) course waste any more of my time.

Luckily for me, in this case. a few months later Kent State happened so that I was able to drop the course that deep into the semester (mid-May) with no consequences, no hit to my GPA.

The next year I'm into Advanced Calculus which I have to drop because it's ALL theory. My beloved differential equations and corresponding numbers were nowhere in sight. And, the Modern Algebraic theories course was deadly. What happened to all my numbers in a math course??!!! The only numbers I was seeing were the problem numbers. What happened to my beloved math I'd love from 1st grade all the way through the Math IV differential equations course? This IS math??!!! Not MY math!

I dropped out of school after that sophomore year.

About 20 years ago I did get my A+ computer technician certification. From all the studying I did for that exam (reading a 1,000 page book twice, among other study materials) I ended up quite well understanding all these bits and bytes! 30 years later!

A story linked to the studying for that certification.

I was in the Yankees Stadium right field bleachers while the Yankees were having batting practice and I was studying for that certification.

I just happened to look up and here was this ball (home run) coming right at me. I saw when it was about 20 feet away from me. I had almost no time to react. I stood up, stuck out my left hand. It hit the palm of my left hand, bounced off, and then a policeman picked it up and gave it to a kid. Now it was starting to hurt a lot. The ball had been going at least 80 mph? And, I had nothing to show for it! I quickly went under the stands and asked for some ice. Got it, put it on my palm and both the swelling and pain rapidly went away. I think it may have been Bernie Williams who had hit that ball.

Went back to my seat and my studying!

Vinny

[Mountaineer]

Good morning. Perhaps this will brighten your day.

https://www.youtube.com/watch?v=BumCkswUUDA

[Xan]

By the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.

It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.

As Kronecker said, "God made the natural numbers; all else is the work of man."

That Kronecker quote kind of gets to the heart of the issue for me. According to Kronecker, God made the natural numbers, which are just the positive integers 1, 2, 3, 4, and so on. Man made the rest, which would include pi, e, and i. (Having said that, I agree that pi for sure seems like a discovered thing, not invented, but I'm trying to run with Kronecker for a bit.)

And yet we come up with all kinds of amazing combinations of these things which were never imagined when man invented them. To me at least that suggests that there is some underlying system to the whole thing. Did that system just happen by chance? Seems unlikely. Maybe Kronecker was wrong. Maybe the whole system was made by God.

I stumbled on an interesting book preview. This particular excerpt discusses how anything other than positive integers were considered "not real", and ways in which even things like adding and multiplying negative numbers don't really make sense. Then it gets to the complex number plane. May have to buy the whole thing.

[stuper1]

That looks like an interesting book, just the kind of thing I like to read. I'll put that on my list.

The author, a Puerto Rican immigrant, has another more recent book that also looks interesting called "The Media Versus the Apprentice: The Devil Mr. Trump". Apparently, as a self-declared non-supporter of Mr. Trump he took a meticulous unbiased look at whether the media has been fair. His conclusion is that Trump is right about "fake news". He says that fiction was often reported as news.

[Xan]

That looks like an interesting book, just the kind of thing I like to read. I'll put that on my list.

The author, a Puerto Rican immigrant, has another more recent book that also looks interesting called "The Media Versus the Apprentice: The Devil Mr. Trump". Apparently, as a self-declared non-supporter of Mr. Trump he took a meticulous unbiased look at whether the media has been fair. His conclusion is that Trump is right about "fake news". He says that fiction was often reported as news.

That also sounds very interesting!

[stuper1]

Despite his many faults, the one thing I am thankful for with the Trump presidency is that it opened my eyes to see how unreliable any of the news media are. I'm including everybody in that list, including Fox. Now I take everything they have to say with 10,000 grains of salt. In my opinion, anyone who believes anything fed to them by the media is quite silly. The media is just out to make a profit like anybody else. If anyone thinks they are giving us unbiased news out of the goodness of their heart then that person is very naive.

[Mountaineer]

Despite his many faults, the one thing I am thankful for with the Trump presidency is that it opened my eyes to see how unreliable any of the news media are. I'm including everybody in that list, including Fox. Now I take everything they have to say with 10,000 grains of salt. In my opinion, anyone who believes anything fed to them by the media is quite silly. The media is just out to make a profit like anybody else. If anyone thinks they are giving us unbiased news out of the goodness of their heart then that person is very naive.

That's one of the things I'm grateful for too.

Me three. I think my favorite equation in regards to the media is U812, there is nothing to equal it.

[Mountaineer]

Good morning everyone. Another beautiful day in the neighborhood here.

I'm grateful today for food and drink, shelter, wonderful wife, and my forum friends. Hope you are all well.

[dualstow]

Glad to hear it, Mountaineer. I’m grateful for the same, but not the ants I found in the kitchen.

[Mountaineer]

Glad to hear it, Mountaineer. I’m grateful for the same, but not the ants I found in the kitchen.

I've had good results with this, better than anything else.

https://www.amazon.com/TERRO-T300-Liqui ... B000HJBKMQ