Math and different number system

[FancyMouse]

3 minutes ago, LN400 said:

But now you are applying our understanding of it to all kinds of maths. Rings, fields, the unit, they are all human inventions or a result of the human understanding to bring order in our understanding of our maths. My point is, we can not assume that our inventions are applicable to all maths. As for the matrices, you just highlighted my point. We are limited in how much we can imagine. That goes for each and every one of us from dumbo to Hawking. We have different limits but that's irrelevant. We all have our limits. We can not imagine what's beyond our limit.

As for that vid, and 1 + 1 = 0, one thing they do mention is modular arithmetics where 1 + 1 = 0 is as valid and as significant as 1 + 1 = 2. The same operation, the same value (1) and 2 distinctly different results. That was one of the points I was talkng about. Now if we can have 1 + 1 = 0 or 2 depending on the rules, then it's false to say that 1 + 1 is always 2. If that is false then who are we to say there aren't other ways to add those 1's to get even more different answers, IF we change the rules.

Your first point sounds like "oh, alien life can have a totally different structure from earth life"

Your second point (or rather, the video's point based on your description) sounds like "oh I can disprove energy conservation because I can change the frame of reference to get different velocities, then kinetic energy changes, but nothing else changed, so energy is not conserved"

I gave up.

[rudi1291]

When you asked about how long to adapt to a new number system, i thought about the Euro, which was introduced as currency in my country when i was a kid, almost 15 years ago. And there are still people who do the conversion to our old currency, if they want to buy something... Yes, its not quite the same as for a different based number system, that might take even longer, but it may give you a lower boundary.

Work with a new system: Maybe within a few years. But really understanding it may take a long time...

Edited March 11, 2016 by rudi1291

[Hary R]

26 minutes ago, rudi1291 said:

When you asked about how long to adapt to a new number system, i thought about the Euro, which was introduced as currency in my country when i was a kid, almost 15 years ago. And there are still people who do the conversion to our old currency, if they want to buy something... Yes, its not quite the same as for a different based number system, that might take even longer, but it may give you a lower boundary.

Work with a new system: Maybe within a few years. But really understanding it may take a long time...

I was in France when that happened and as you said, different people adapt at different pace, I was fortunate be be one of those of think: euro it is now, no need to think in franc anymore. But I know some people from back then who needed to convert first. 

Off topic, do you know the jock about a french guy who want to buy something in Spain, he first convert his french euro in franc, then convert it to spanish peseta and finally he convert it to the spanish Euro.  

 

[K^2]

On 3/10/2016 at 2:13 AM, LN400 said:

But now you are applying our understanding of it to all kinds of maths, you even say "defined as".

Not all the mathematics. Just groups, rings, and other algebras which are required to have units. Without identity, you would be talking about a quasigroup or a semigroup, for example. Or even just magma in general.

Trust me, if you've thought of something, mathematicians have considered it over 200 years ago and incorporated it into general mathematics theory. Any assumption we take for granted with what we usually think of as maths has been evaluated, and theory with different assumptions certainly exists out there somewhere. Some of these even find practical use.

[LN400]

7 hours ago, K^2 said:

Not all the mathematics. Just groups, rings, and other algebras which are required to have units. Without identity, you would be talking about a quasigroup or a semigroup, for example. Or even just magma in general.

Trust me, if you've thought of something, mathematicians have considered it over 200 years ago and incorporated it into general mathematics theory. Any assumption we take for granted with what we usually think of as maths has been evaluated, and theory with different assumptions certainly exists out there somewhere. Some of these even find practical use.

I don't consider myself to be the one to come up with anything groundbreaking in maths. I never did. Anyone thinking I did have not understood any of what I've been saying. My point was, and still is, the way we humans see maths is, neccessarily so, limited by the way our brains have evolved, how the brain is wired. Our brain is in no way something that evolution will always strive to evolve elsewhere That kind of idea is pure anthropocentricity, or if you like, our tendency towards species narcissism. We have our maths and that's fine but to rule out that maths can exist that is beyond human understanding is, to put it mildly, extremely pompous and pretentious.

Edited March 14, 2016 by LN400

[pincushionman]

How did we get from "can we do the same math in a different number system?", which is a valid question but the answer is well-understood, to "I think we actually don't understand math", which willfully ignores what modern "pure" mathematics research is aboout (being "find out where our understanding breaks down and find ways to patch it up when we find those places")?

[Hary R]

5 minutes ago, pincushionman said:

How did we get from "can we do the same math in a different number system?", which is a valid question but the answer is well-understood, to "I think we actually don't understand math", which willfully ignores what modern "pure" mathematics research is aboout (being "find out where our understanding breaks down and find ways to patch it up when we find those places")?

De facto, my original question have been answered and the post above is more of philosophical question than a science one as their is no way to be sure who is right unless an alien life form come and demonstrate that what they have a different vision of math. (or the same)

 

PS: by the way, the question was more, "can we understand the same math done with a different number system".

[LN400]

Sorry for any derailment of this thread

[wumpus]

https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/

My guess is the this is either a hoax or an example of p-fishing gone hilariously wrong.  Nevertheless, I'm sure vast armies of cranks will research this dry, and might just discover a few things about "math different number systems".

Note - the link goes to a paper popularizing a paper that claims that there are distinct differences of the probabilities of last digits of the next prime depending on the last digit of the preceding prime.  Should this be real, it would be interesting to see if it extends into other number systems and if it extends any further than the authors were able to check.

[FancyMouse]

20 hours ago, K^2 said:

Just groups, rings, and other algebras which are required to have units.

Just want to mention that from what I've been taught in college, not all definitions of rings require unit/unity/1. Wikipedia definition seems requires that, while many of the textbooks I've seen don't (and explicitly say terms like "commutative ring with 1" all the time).

Of course, it doesn't change anything other than how we call things, just like Pluto still being Pluto. But still, good to know it in case it helped for reading a paper.

[K^2]

17 minutes ago, FancyMouse said:

Just want to mention that from what I've been taught in college, not all definitions of rings require unit/unity/1. Wikipedia definition seems requires that, while many of the textbooks I've seen don't (and explicitly say terms like "commutative ring with 1" all the time).

Conventions on that sort of things seem to be in a bit of flux. Modern convention is to include multiplicative identity in the definition of the ring, with these algebras lacking identity getting called something like pseudo-rings.

But yeah, good call on watching out for it. It's kind of like m in modern physics representing rest mass, whereas some of the older papers, especially these written by Einstein himself, used m as the symbol for relativistic mass. Rest mass in such papers is denoted as m₀. And if you don't know about it, it can cause much confusion. Like with the E = mc², which is absolutely true with Einstein's notation and not generally true with modern notation.

Fortunately, once you are aware that these things are out there, figuring out which convention is used is easy from context.