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Mathematics must include all of its branches and that would include arithmetic. So say, multiple objects existed and were observed. That, however, doesn't make mathematics a discovery. It is the association of multiple objects as a group, and making that initial "one and one are different than one" ( . . . and we'll so note it . . . ) that is where mathematics begins.
This is conceptual - and thus - an invention. Two rocks sitting near one another does not have to be thought of as two rocks. Why not simply "A rock" and "A rock" ? That still works. At the same time, they may not be near - but one could still conceive of them as two items that are in some (conceived!) category and then associated.
Our mathematics is a description of observations - and not necessarily the only way one could describe the universe.
| "The difference between genius and stupidity is that genius has its limits." - Albert Einstein | | "As far as we know, our computer has never had an undetected error." - Weisert | | "If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010 |
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W∴ Balboos wrote: Our mathematics is a description of observations - and not necessarily the only way one could describe the universe.
No it isn't. You cannot observe a circle, (or any geometric shape come to that), because a circle is inscribed with a line of zero width equidistant at all points of zero dimension from another point of zero dimension. You cannot observe infinity (obviously) or zero or the square root of -1. It's dubious even whether you can observe number in any real sense. Mathematics is merely a system of logic. Any resemblance to real physical phenomena is entirely coincidental!
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Official Pun Reply:
You can count on a number of possible answers.
| "The difference between genius and stupidity is that genius has its limits." - Albert Einstein | | "As far as we know, our computer has never had an undetected error." - Weisert | | "If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010 |
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Watch this: [^]
I would say: Math is.
Kitty at my foot and I waAAAant to touch it...
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Discovered 
1. Mathematics is the language of nature.
2. Everything around us can be represented and understood through numbers.
3. If you graph these numbers, patterns emerge.
Therefore: There are patterns everywhere in nature.
from PI[^]
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There's only one thing wrong with that. Every word you've written!
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Mathematics is a cognitive virus which jumped from fleas to early hunter-gatherer hominids in the late Paleolithic, driving said hominids to evolve to be able to count up to twenty (ten fingers, ten toes) quickly. The proto-human hosts reached a modus vivendi with the virus since such counting was useful when figuring out who to kill next, or, who to enslave next.
Since it is an insatiable virus, it soon turned its early homo sapiens hosts into shepherds and farmers where there were more things to count (goats, cattle, sheep, baskets, sheaves, jars).
At this late stage of human co-habitation with Mathematics virii, it is safe to say it is as much an archaic endosymbiotic part of our nervous-system as mitochondrial DNA (once single-celled organisms "captured" by Eukaryotas) is a part of our cellular structure.
The rare human being in modern times who is able to free themselves of the Mathematics virus completely is usually considered an idiot, or insane, or becomes the founder of a new religion. Their lives are short, and their death often violent.
Mathematics appears able to mobilize its hosts into insane clown posses which collectively attack external threats; the exact mechanism by which this social-engineering occurs is not clearly understood, probably because those who reach the point where they could explain it are murdered, or "disappeared," or sent to mental asylums.
Cantor and Godel are good examples of Mathematics defending itself by directing the minds of those rare geniuses who realize what Mathematics actually is into the black-hole of considering the relative magnitude (ordinality, "Aleph") of infinities. Both, these brave souls ended their lives in mental illness, haunted by fears of being poisoned.
Well, what can you say about something that you can't imagine yourself, or the world, without ?
Without Mathematics we would be ... what ? ... as happy as dogs?
cheers, Bill
«I want to stay as close to the edge as I can without going over. Out on the edge you see all kinds of things you can't see from the center» Kurt Vonnegut.
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As the relationships are discovered, a language for describing them is invented.
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Math was invented.
One day, many years ago, a man at prayer was doing his usual thing when a winded messenger from the King came across him praying in a garden. "I've a message for the Prince but I'm exhausted and can continue no further, will you take it to him? It's a matter of national security". Hemming and hawing for a moment, the man at prayer realized it would be to his advantage to help the King in any way he could so he replied "Yes, I'm done praying for the day. Give me this message and I'll take it to the Prince". The messenger reached into his belt pouch and pulled out the coil of leather upon which was scribed a long sequence of characters. "Here, here it is. Under no circumstances is this message to fall into enemy hands for it would compromise the King, the Prince, and every citizen in this land. Take it.
"Oh, but this is too heavy" said the ostensible bearer. "I can't add this to the array of weights my already overburdened frame can support. What with running ... I've got to carry all this stuff too; how will I ever get anywhere? I'll fail at the task, the scytale will fall into the possession of the enemy, and worse yet, I'll have my hands cut off for being on the wrong side, once they decypher it's meaning".
Well, by now, the messenger had begun to recover his strength and was looking a little less peaked in the cheeks. "That's ok. I'm feeling rested now. I'll continue on. I'll do it. Deliver the Kings' message to the Prince." And with a glance up ahead, he got up off the ground, stood on his own two feet again and ran away.
"Phew" said the man to himself, left behind in the garden. "For a minute there, I thought I'd have to actually run with this message to the Prince". And with that he returned to his prayers. Quickly he realized he was done, packed up his things and headed for home.
(The invention of math came to us in the ensuing moments after the brief encounter between the runner and the praying man. The runner got the idea that as long as he kept ahead of the enemy, by taking short breathers along the way, he'd do his job. And get paid. The man praying became lost in the thoughts about being held accountable for the non-delivery of a message entrusted to him by constabulary authorization of, presumeably, a member of the King's court, the loss of both hands, probably a very bloody and painful proposition, and likely his own death. Also there was the fact that he, only a man of prayer, would never get paid for doing this nice thing for the messenger, had he actually managed to stay alive after the intial traumatic ordeal. Not to mention the fact that there was the thinking about how he didn't really have to overburden himself with added weight. All he really had to do was run back to the King, obtain the stick upon which the scytale was originally enscribed with the secret message, reenscribe it, this time in a more secure method, and on something not even a smart enemy would ever think about enscribing code upon in the first place, the man's philactory, and continue back to the spot where the original was entrusted to him, and continue on to deliver it to the Prince.)
I'll have to cut this short. I've got a moral to deliver. Turn over see reverse side for moral.
modified 19-Aug-15 15:39pm.
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Your imagination just invented an up-vote from moi. cheers, Bill
«I want to stay as close to the edge as I can without going over. Out on the edge you see all kinds of things you can't see from the center» Kurt Vonnegut.
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I will have to say, this is straight to the point! 
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42
New version: WinHeist Version 2.1.1 new web site.
I know the voices in my head are not real but damn they come up with some good ideas!
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I wonder why it came to that question?! 
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This is a rant, so you don't have to read further if you're not interested.
I am sick and tired of constant software updates! Firefox's monthly updates, Adobe Acrobat, Java, and, of course, Windows and Linux OS updates and the myriad of other software that nags me every few minutes about "security" updates and program fixes.
This is taking up to two hours a day to maintain a limited computing environment! So, I can't even begin to imagine the hell that IT managers in big corporations might be going through!
But, the worst part is when they slide "opt out" selections, like Java updates sliding in MacAfee security in their updates. Miss the opt out and you're dinked!
Or, they slide promotional software nags, like the Windows 10 upgrade nag into "security" fixes for Windows 7 and Firefox's "make Yahoo my default toilet paper".
If their software is that bad that there are that many bugs and security breaches, maybe, just maybe, they had better get their a$$es in gear and figure out a better way!
And there is a better way! I just don't have time to develop it because I'm too busy installing updates!
Rant over! We now resume regularly scheduled programming.
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Quote: two hours a day
Hyperbole is allowed in a rant. We all understand that. But ... 
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There's a way to avoid all these updates. It's simple and easy: Unplug your WIFI cable. If you ain't got one you can get one on eBay or amazon or send me your money and see what you get.
Kitty at my foot and I waAAAant to touch it...
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Yeah, for the reasons cited by the OP I gleefully call them Automatic Corruptdates. If they don't screw up the moment, start-up, shut-down or anything in between, if all is not right with the corrupdate or your system or the spirit world's assessment of you at that moment, things could be as bad as a black screen and perpetual blinking cursor.
That said, botched update application accounts for about 20% of revenue for my Mom n' Pop PC shop.
Security Update my a$$ Microchump. What did you put on my PC there?
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Yes it's pretty annoying. I tend to keep my work PC hibernated as I usually have a load of "stuff" open, and I keep my home laptop hibernated because it takes an hour to start up. Having to reboot to install constant updates is annoying. When you shut your laptop down and it pops up "Installing update 1 of 23...." 
Java trying to get you to install things is well annoying, but not as annoying as that time it updated java and Solr stopped working as the new version was not compatible. Picture a Microsoft dev trying to work out how to get a specific version of java and configure Solr to use it....yeah, not fun.
It's also a new attack vector as you get those rogue sites that look identical to the Adobe or java "update to the latest version" screens. It won't fool me (the porn site that spawned it uses html5 to play vids, not Flash), but I bet it fools many others.
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rjmoses wrote: If their software is that bad that there are that many bugs and security breaches, maybe, just maybe, they had better get their a$$es in gear and figure out a better way! And there is a better way! I just don't have time to develop it because I'm too busy installing updates!
Proving software is bug free is equivalent to solving the halting problem. Let me know if you make any progress on that after you stop patching your box, I won't be holding my breath.
Did you ever see history portrayed as an old man with a wise brow and pulseless heart, waging all things in the balance of reason?
Is not rather the genius of history like an eternal, imploring maiden, full of fire, with a burning heart and flaming soul, humanly warm and humanly beautiful?
--Zachris Topelius
Training a telescope on one’s own belly button will only reveal lint. You like that? You go right on staring at it. I prefer looking at galaxies.
-- Sarah Hoyt
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My android has been nagging me for a long time now to do a system update and sure there may be some important security fixes but most likely it will just F*up my layout and settings.
Java and Adobe is the worst I think.
I tend to ignore updates until I absolutely must. The last time I updated a non security update on windows 7 I got a buttload of networking issues at my home computer.
I think software that often pushes updates messages should be labeled gloatware.
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rjmoses wrote: This is taking up to two hours a day
Time to change that 56k modem for something better...
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Yeah, right! Windows 10 "update" on test system == 450+MB. Failed twice! Bull feathers!
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rjmoses wrote: Firefox's monthly updates
If only. They update it a lot more often than that.
rjmoses wrote: Adobe Acrobat, Java
Haven't had either installed on any of my machines in at least a decade.
rjmoses wrote: This is taking up to two hours a day to maintain a limited computing environment! So, I can't even begin to imagine the hell that IT managers in big corporations might be going through!
They let the machines update themselves. If you're actively "taking two hours a day" dealing with updates, you're doing something very, very wrong.
I can't speak for third-parties, but if you want to get at least the Windows updates out of the way, but you still want to selectively control which updates get deployed or not, have a look at WSUS. For my own home LAN (8 physical PCs or so, plus many times that many virtual machines), it saves me a lot of bandwidth, and I only have to click Approve or Decline once on Patch Tuesday, or whenever there's an out-of-band update. I can live with that.
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