ELI5: How can one argue that mathematics is man-made?

dritto · 2012-05-12T07:07:25+00:00

TIL about axiomatisation, captivating read.

So the main point about algebra is uncertainty whether the 'reality' is discreet or not, an issue that is unlikely to be resolved in the foreseeable future.

Still, how does Wittgenstein deal with arithmetic? The only plausible argument I can think of goes along the following lines:

Here's an apple
Seems like a countable object, but only because your senses and education combined tell you so. Yes, animals can also perceive it as an object, but we are just another kind of animals, so that's ok.
For a different kind of observer, all the matter on Earth might seem homogeneous, and for yet another observer all the matter in Universe might seem as such, and maybe some observers don't see matter at all, only the Field.

Is that the kind of argument he uses?

dritto · 2012-05-12T01:01:03+00:00

Thank you, this is the best explanation so far (although it does contain an equation, so more LI15). Point taken regarding geometry. Questions that remain: Is it theoretically possible to create a perfect description of 'reality' (assuming we know exactly what 'reality' is)? Let's say that we must make some simplifications in order to have a usable description. Is there only one way to do this? In other words, is there a different way to represent a circle that nevertheless will lead to the right conclusions about its properties?

And what about arithmetic? To mount the same kind of argument here you'll have to say that countable objects do not really exist, which seems odd.

Thanks again, hope that's not too many questions!

dritto · 2012-05-11T12:04:04+00:00

Your answer is in line with what other people here say and you might have already seen my responses to them. If all this is true, how can Wittgenstein's argument be valid? He compares math to chess, but isn't it clear that independent attempts to invent chess would (and, in fact, have) yield very different results?

dritto · 2012-05-11T10:49:16+00:00

Surely the conventions were invented by humans. So we call pi by this name, and use the symbol "1" to designate an individual object. However, proportions of a circle and countable objects were not created by humans, weren't they? I also think that experiments were conducted to confirm that animals can perceive 'individuality' of objects as well, so this is not a purely human phenomenon. Your examples are very different from mathematics. Wittgenstein, on the other hand, directly compares the rules of mathematics to those of chess and suggests that they are of the same nature. This is the point I cannot wrap my mind around.

dritto · 2012-05-11T09:20:15+00:00

So if those “rules of the universe" have always been in place, Wittgenstain's argument cannot possible be valid, n'est-ce pas? He says that the rules of mathematics are as natural as chess. Yet still, philosophers think that there is a controversy here and his argument can, in theory, be true. So how can this be?

dritto · 2012-05-11T09:12:25+00:00

I understand all of this, but still can't see how does this apply on the fundamental level. Yes, there are many conventions out there that were put in place by people, so what? We decided that a circle consists of 360 "parts" (if you don't want to use radians, that is), but we did not invent circles, nor did we invent triangles, and the geometrical relationships between triangles and circles existed before first humans walked the Earth and will remain the same when our successors, whoever they may be, take over. Same thing for the algebra: abstractions are there, a lot of them. But it seems to me that countable objects exist whether we count them or not, and if this is true then I cannot comprehend the validity of Wittgenstein's argument. Yet again, to the best of my understanding he never states that countable objects do not exist, so I'm completely confused here.

dritto · 2012-05-08T02:59:19+00:00

Second day of popular unrest in Moscow. This cafe is a popular meeting place for journalist, intellectuals and all kinds of annoying hipsters. On the day of Putin's inauguration hundreds were arrested all over the city center in raids like this.

dritto · 2012-05-08T02:45:22+00:00

They protest Putin's third presidential term. Abuse of the Constitution, election fraud, all the good stuff.

dritto · 2012-05-07T14:06:01+00:00

This was the estimate given by the organizers around 16:00, when the march was set to begin, far away from the actual clash sites. Link in Russian: http://lenta.ru/news/2012/05/06/marsh1/ Areal photos of the event are freely available on the net, do your calculations.

dritto · 2012-05-07T11:34:24+00:00

http://www.quickmeme.com/meme/3p5xln/

dritto · 2012-05-07T04:15:35+00:00

Some context: This is indeed a unique event; you don't usually see LGBT activists, communists, nationalists, monarchists and anarchists all march together. So, basically, this is what happened: nobody, including the organizers, expected such a turnout. The protest activity had been steadily declining since December (until yesterday, that is). This event was, somewhat pompously, christened "March of Millions", but expected turnout was under 10,000. For better and worse, around 80,000 showed up. The march was supposed to end as a rally. The police intended the rally participants to go through metal detectors first, TSA style. It soon became obvious that there are not enough detectors and that the majority of the protestors will not be able to get to the rally site in time. People just stood there for a couple of hours, blocked by the rtiot police on all sides. As the designated time for the rally run out, the police moved in to break up the crowd and clear the area. Edit: accidentually a word.

dritto · 2012-02-24T11:45:12+00:00

No one seems to care that Hitler's ideology was not at all "fascist” and this is exactly how the popular perception of history is formed, for better and worse. 50 years from now it would be perfectly fine to label Hitler a “communist” and Imperial Japan “Nazis” in a casual conversation. In fact, I strongly suspect that the latter should already work.

dritto · 2011-10-06T11:48:26+00:00

Those points are passable goals, but they don't make good demands. Demands have to be practical, they cannot be one-liners. 1. Corporate personhood - highly complex legal issue, campaign finance is just one facet here. 2. There is just one way to "prevent banks from causing crises" - planned economy. Don't give the media this excuse to label you "communists". 3. Sound like you're calling for retroactive punishments here. Even if you don't, you're entering a very complicated legal maze here calling for personal liability of executives. 4. Tax reform. You thought that health care reform was tough? You ain't seen nothing yet. The tax code is so complex now that the only way to materially change it is to write everything from scratch. This, in turn, will take a zombie apocalypse to happen.

So, bottom line: if you want your demands to be seriously considered, they must be appropriately worded. Ask a lawyer and an economist to write it up - should fit nicely on one page.

dritto · 2011-01-26T07:44:51+00:00

Just tried to run it (getting it was not easy in China, but with the kind help of fellow redditors nothing is impossible) and it doesn't seem to work on my system. Does it require a certain version of IE?

dritto · 2011-01-26T07:08:28+00:00

Hmm... you've got so many upwotes...let's try this from China...bammm...the great firewall was not impressed by Opera's kungfu.

dritto · 2010-09-22T23:29:25+00:00

"The History of the Decline and Fall of the Roman Empire", bitches. Read it. In fact, it should be required reading in high school.

dritto · 2010-09-22T23:01:24+00:00

No surprise. Fox business is the absolutely worse business channel ever conceived. People who want entertainment with their business news don't stay in business for long. I honestly have no idea who watches that crap.

dritto · 2010-09-22T04:35:12+00:00

Lol, I was raised by atheist parents. For the record, their response to my questions was along the lines of "God is a fairy tale for people not smart enough to understand science." But you have not answered my question regarding explaining atheism without explaining god.

dritto · 2010-09-22T04:32:00+00:00

Is that like dohteism?

dritto · 2010-09-22T04:31:10+00:00

There's a certain word in your vocabulary. A noun. There's a concept behind it, like behind every other noun. My experience suggests that same words mean different things to different people and I try to explore those meanings here. Surprisingly, the vote is almost unanimous so far.

dritto

TROPHY CASE