Capt Ayhab

Invention/Discovery

Here I am more inclined to Dash Kapitan's statement that it is both invention and discovery. (takyeh bar jayeh bozorgan natavan zad amma!)

Invention in the sense that maghshoosh and Azarin write about. Math is a language invented to describe nature. Even in cases that it has no immediate use, some times later it can be used to describe nature. Non-Euclidean geometry being one example, it existed before Einstein used it in his general relativity. But, then math is also in the nature without any of our constructs to explain it. This I can best explain by the existence of fundamental physical constants.

Another riddle

OK, I'm letting myself to be dragged into this. As Borg would say "resistance is futile"!  Here you go: 

There is a prisoner in a cell with 2 doors, one will lead to the Freedom and the other will lead to the Torture chamber. Both doors are identical and you do not know which door will lead to which. In front of the 2 doors are 2 security guards. One will ALWAYS lie while the other ALWAYS speaks the truth.

You must ask ONE question for you to find out which door leads to freedom or torture. Any type of questions but only one.

Maghshoosh jan,

I'll still keep your Field Prize handy here in case you found a closed form for that probability, or in case you found a book with a larger margin. Fermat's was the book of law, what is your?

1 + 1 = 3 or ....

Here is my invention ;)

1 + 1 = 3  or 1 + 1 = 0

1=2

Ok lets say a=b

Then a^2 =a*b

add a^2 to both sides and you get 2a^2=a^2+a*b

then subtract 2a*b from both sides: 2a^2 -2a*b=a^2 +a*b-2a*b

2(a^2-a*b)=(a^2-a*b)

now you can omit (a^2-a*b) from both sides and what do you have?

voilà!  2=1

I know I know you can't omit that unless a^2 is not equal a*b, hence (a not equal to b) which negates your initial assumption.

But since roman numbers are decimal these days, I figured what the heck! ;-)

IRANdokht

Fermat's real last theorem.

ID & Jaleh, That dufus who preferred to remain anonymous and who claimed to have a general solution for the 2-coin-deficit problem is patently misguided. I checked his proof that he'd forwarded me and there were holes in it you'd go dizzy looking into. Boy, must his face be red, though at least, he did say that he hadn't double-checked his hasty calculations. It's a complicated calculation that I've successfully completed, but the margins here are too narrow for it.

Language & math

Azarin S., I was skirting around the discovery/invention "duality" by calling math a sort of "language." Your statement that "Mathematics is a pure invention of human beings, like any language" may need elaboration. It's true that any language has arbitrary inventions in it, such as choice of words and sounds. But it is widely accepted that there are rules of language that are common to all of them and are characteristics of the human brain. I'm no expert on this but it's argued that all languages are generated based on some common rules governing the operation of our brains, though such rules are not fully understood.

It's also logically possible, that our brains could have evolved to have the capability of language but not mathematics as we have today. Then we would not have had the proper language for the deep secrets of the universe. Personally, I suspect that the capabilities of generating mathematical concepts and language are related, but just a guess. Also, in all likelihood there are aspects of nature that we will never understand even using mathematics; we're just not capable of generating any language for them.

I'd say an invention!

I'd say that the mathematics is an invention and not a discovery.

I still remember my Math teacher at the University of Bourgogne (it was so many years ago!) trying to help us with our confusion over the concepts defined in our Topology class (I confess: his advice didn't really help me!): He said that our biggest mistake would be to try applying these topological concepts (applicable to an n dimensional space) into the 3 dimensional world (aka nature)!

Other example would be just the simple concept of negative numbers that cannot be found in the nature, so the simple equation of 1-2=-1 is one of the most important of abstract concepts!

So, I think the Mathematics is a pure invention of human beings, like any language. And the numbers are its alphabets.

Now, I'm shaking (the way I used to shake before getting my results back from my professor (= Captain Ayhab here)...:-)

Azarin

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but but but Captn'...

half of 12 = 7 

was a mathematical question that I answered!

you should have just accepted it gracefully and left the "lets-circumcise-some-Roman-numerals solution" (thanks Maghshoosh jan) idea alone all together cuz roman numerals ain't decimal your hint was not accurate after all. 

:o))

IRANdokht

200 hits?

New Problem

1=2

-YT

Maghshoosh

To mano belakhareh pir mikoni lol

You have a point, I did not make myself clear. But let me be cheeky and answer the question with another question.

Is FIRE and invention or a discovery?

To me an invention is NOT a creation , rather it is configuration, or composition of matter, device or discipline. Discovery on other hand is observing or finding something unknown to one's culture.

As to my [half of 12 = 7] since it is not even a mathematical problem therefore is not an invention, nor a discovery.  It is just -YT playing a smart ass. ;-)

-YT

Flying Solo into invention and discovery

Ms. FS,
As far as its use in the natural sciences, math is the language our minds use to discover and express the underlying laws of nature. We don't know of any other language or means of expressing much of the deep facts about the universe. You can ask the same question about logic, which helps us make sense and organize what we observe around us. Is logic part of nature or an invention of our minds? I'd say these are languages that enable us to uncover facts inherent in nature.

Also, not all theories and models in mathematics are applicable in describing nature. Pure mathematicians come up w/ theories in mathematics that may not have any application in science. Think of a usual language. You can form sentences that are perfectly consistent w/ the rules of the language, yet convey no sensible meaning. Mathematical theories may have meaning w/in their own logical framework and assumptions, but not necessarily in terms of laws of nature.

علی جی

دقیقاً..... ایول!
و علت اینکه بجای ١-١٢ شماره بندی کردن توپ  ها من الفباء رو پیشنهاد کردم ؟ میخواستم ذهن بقیه رو بطرف احتمالات دیگه هم سوق بدم !!
(آخه مرض دارم)!

راجع به جوابهای دیگه در مورد مسئله من که هیچکدوم کامل ( ٣/ ٣ ) نبود......
دو تا دهاتی داشتند راجع به روش تدریس سپاهی دانش ده شون گله می کردن، یکیشون گفت:
والله مش غضنفر چی بوگوم؟ به پسره مِگُم برو گوسفندانَه بشمر، مِرَه دِ علفزار....  دِمَرو رو  زِِمِن مِخوابَه.... پاهاشونهَ مِشمرَه... اووخ  تقسیم به چار مِکونَه!

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Maghshoosh, your formula for 2 coin deficit

Your formula appears to not agree with my result with n=2. When I work it out for the case with 2 and 4 coins (n=2), I get 21/32 as the the probability we are looking for, while your formula yields 43/64, a tiny little mismatch of 1/64. I calculate my answer by first conditioning it on the no. of Heads obtained by the 2-coin guy (0, 1, or 2). You get 1/4*15/16+1/2*11/16+1/4*5/16 = 21/32.

There seems to be an issue with the constant 5 in the formula I believe. I'll look into it later tonight (after 11 pm EST).

Discovery or invention?

Captain, Your response to Flying Solo seems incomplete. You claim that math is both an invention and a discovery. One of your arguments is that math is in the design of the universe. That makes it a discovery, b/c it's already there in its final form & we're just unveiling it. Then you give another argument of why it's a discovery b/c of something about humans' use of it (which I didn't quite get). So where is your argument that it's also an invention?

As an example, Irandokht's elegant and mathematically-savvy base-12 solution of the "half-dozen=7" puzzle is more of a discovery, whereas your lets-circumcise-some-Roman-numerals solution is more of an invention of an imaginative mind.

Solution to Majids problem

ok Majid

here is the freaking solution!!

You wasted 2 hours of my time at work, but it's cool I got entertained. LOL
Non of my coworkers have been able to solve this yet. hahahahahaha
I had a typo in my first post I fixed it though. This should be good now. :)

First of all I don't know how you expect to explain this using 3a, 3b, 3c ...
The problem is far more complex than that!!!! BTW my solution will tell you which one is the odd ball and wether it's heavy or light. :P

This is what you will need to do.
1 2 3 4 5 6 7 8 9 10 11 12
fyi: each dash represents a use of the scale.

(1 2 3 4) (5 6 7 8) (9 10 11 12)

-(1 2 3 4) = (5 6 7 8)

--(1 2 3) = (9 10 11)
---1>12 12 is the light ball
---1<12 12 is the heavy ball

--(1 2 3) >(9 10 11)
---9=10 11 is light
---9>10 10 is light
---9<10 9 is light

--(1 2 3) <(9 10 11)
---9=10 11 is heavy
---9>10 9 is heavy
---9<10 10 is heavy

-(1 2 3 4) > (5 6 7 8)

--(1 5 6) = (2 7 8)
---1 = 3 4 is the heavy ball
---1< 4 3 is the heavy ball

--(1 5 6) > (2 7 8) Then either 1 is heavy or (7 8) are light
---7 = 8 1 is heavy
---7 > 8 8 is light
---7 < 8 7 is light

--(1 5 6) < (2 7 8) Then either 2 is heavy or (5 6) are light
---5 = 6 2 is heavy
---5 > 6 6 is light
---5 < 8 5 is light

-(1 2 3 4) < (5 6 7 8)

--(1 5 6) = (2 7 8)
---1 = 3 4 is the light ball
---1< 4 3 is the light ball

--(1 5 6) < (2 7 8) Then either 1 is light or (7 8) are heavy
---7 = 8 1 is light
---7 < 8 8 is heavy
---7 > 8 7 is heavy

--(1 5 6) > (2 7 8) Then either 2 is light or (5 6) are heavy
---5 = 6 2 is light
---5 < 6 6 is heavy
---5 > 8 5 is heavy

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lol

I thought a bit of mind game wouldn't hurt.

Ma mokhlesim khanoom lol

-YT

ok Majid here is the

ok Majid

here is the freaking solution!!

You wasted 2 hours of my time at work, but it's cool I got entertained. LOL
Non of my coworkers have been able to solve this yet. hahahahahaha

First of all I don't know how you expect to explain this using 3a, 3b, 3c ...
The problem is far more complex than that!!!! BTW my solution will tell you which one is the odd ball and wether it's heavy or light. :P

This is what you will need to do.
1 2 3 4 5 6 7 8 9 10 11 12
fyi: each dash represents a use of the scale.

(1 2 3 4) (5 6 7 8) (9 10 11 12)

-(1 2 3 4) = (5 6 7 8)

--(1 2 3) = (9 10 11)
---1>12 12 is the light ball
---1<12 12 is the heavy ball

--(1 2 3) >(9 10 11)
---1=2 3 is heavy
---1>2 1 is heavy
---1<2 2 is heavy

--(1 2 3) <(9 10 11)
---1=2 3 is light
---1<2 1 is light
---1>2 2 is light

-(1 2 3 4) > (5 6 7 8)

--(1 5 6) = (2 7 8)
---1 = 3 4 is the heavy ball
---1< 4 3 is the heavy ball

--(1 5 6) > (2 7 8) Then either 1 is heavy or (7 8) are light
---7 = 8 1 is heavy
---7 > 8 8 is light
---7 < 8 7 is light

--(1 5 6) < (2 7 8) Then either 2 is heavy or (5 6) are light
---5 = 6 2 is heavy
---5 > 6 6 is light
---5 < 8 5 is light

-(1 2 3 4) < (5 6 7 8)

--(1 5 6) = (2 7 8)
---1 = 3 4 is the light ball
---1< 4 3 is the light ball

--(1 5 6) < (2 7 8) Then either 1 is light or (7 8) are heavy
---7 = 8 1 is light
---7 < 8 8 is heavy
---7 > 8 7 is heavy

--(1 5 6) > (2 7 8) Then either 2 is light or (5 6) are heavy
---5 = 6 2 is light
---5 < 6 6 is heavy
---5 > 8 5 is heavy

my bad...

I didn't know roman numerals were decimal!

dashtim ostaad?

:o))

IRANdokht

half of 12 = 7?

12 in roman numerals = XII

XII<------- half it right where the arrow is and wallah you have VII = 7

-YT

Solo

Little bit of both I think. I say both because the universe  can be explained by mathematics, therefor it is in its design.

It is a discovery, because human beings discovered using it, and have been applying it to explain universe.

-YT

Question

This is an amazing thread. 

Can somebody attempt the answer to the following:

Is Mathematics an invention or a discovery?  Please explain. 

Can you check ...

Jaleh, can you check your 2-coin-deficit problem for the case when the players have 2 & 4 coins respectively? Maybe even 3 & 5 coins? What are the probabilities? I'm beginning to suspect that I may have been too hasty w/ my formula, and eghteshash is pervading my whole being.

Really Irandokht, as if one was not enough!

First he kills Mr. Anonymous on, now he's going to disappear on us by wandering in sex blogs!

I tell you, you let these guys go free with a murder, they extend 1 to 2 and before you know it, you'll have a genocide case on your hand!

Jaleh joon

With your last comments you just made my day!

You go girl!!  :o))

got to go to work... I am so late!

see y'all 

IRANdokht

maghshoosh jon,

"Jaleh, what's w/ a sex blog that's "on top," as you put it? Maybe I should start posting proofs there to induce eghteshashe ravani."

We were talking about another blog called "khyanat Kardam" which had lots more comments than ours. Now we are 174, and they are in 160 range. AND NO, top or bottom, you ain't going nowhere, you stayin right here, hear me?!