Hello LW
Whilst I'm not a mathematician, I
am a software engineer, and that explanation of addition as a function seems pretty straightforwards to me.
From the page:
An empty set in this system is recognized as the ultimate combination of all sets. And naturally, the values on either side of zero are less than the whole set that is zero.
So the only difference is that what previously looked like addition now becomes, in a way, subtraction (and vice versa). In this system, +1 is a "larger" number then +2.
Again from the page:
In the same way that there are two distinct forms of order in nature, there also exists two entirely different ways of seeing zero and all other numerical values. It is a whole other type of value system, a system as valid as the one we presently use, one of no use within the abstract world of individual things, yet immeasurably valuable in cosmology where a mathematical value for the universe as a whole is of critical importance in any attempt to understand for example, the implications of the many worlds theory.
So the author is basically admitting that if we try to apply this number system to the normal world of "individual things", its useless.
It seems to me that the author is doing the arithmetic in terms of normal natural numbers and then adding some philosophical sounding magic on top of it.
Yes. Or maybe magical-sounding philosophy.
From the page....
Our present mathematical system is based upon a perspective derivative of grouping order, or thingness. This unique mathematical system, which we will continue to explore, is derived from symmetry order, its foundational axiom reflecting the innate singleness and wholeness of existence. As a perspective it doesn't see isolated or separate objects. Although its values are definitive, it does not see finite things.
It sounds to me like the author is aware of the sort of problems you are talking about. When we think of "thing A" and "thing B" we are seeing finite, individual, things - and we can add them together and get the sums of those things. The author seems to have admitted that this system is no use in this case. So you just continue to use normal mathematics most of the time. He isn't suggesting we use symmettry math for the things we currently use normal maths for. He has invented the system in order to apply to cosmological problems issues MWI.
The very concepts of addition and subtraction seem to have new meanings under this system. "Addition", as you've described it, depends on starting with nothing (the smallest possible value) and as you add things to it the number gets larger. These two conditions can't be emulated in this system. In this system, the smallest number is -infinity, not zero. So if you wanted to still start with the smallest number you would have to start with -infinity (an infinitely small number) and start adding things in the same way your function already does. But you would never reach zero because there are an infinite number of numbers between -infinity and zero. On the other hand, if you wanted to still start with zero then the problem is that as you "add" units to zero, the value of the numbers is decreasing rather than increasing, making it sound like subtraction instead of addition.
I can understand why somebody well versed in normal mathematics might find this system both very strange and practically useless for nearly all of the things we use normal numbers for. But if we are going to be fair on the author, shouldn't we judge his system by its usefullness for dealing with the cosmological problems he claims it is usefull for?
And he has also added positive and negative infinities into the set of numbers. So, if you use "symmetric maths", you haven't actually gained anything but you have lost consistency since trying to treat infinities with the same rules as finite numbers will not work.
Well, we haven't really given the guy a chance to see whether we gain anything. Firstly, I don't know how best to respond to the technical questions you've raised, and since it's not my system I'm not going to offer any solutions. However, if the system can indeed by applied to cosmological problems and make them less intractable, then we would have gained something. And we haven't lost anything because we can still use normal maths in normal situations - the author isn't trying to replace normal maths.
So the justification for doing this seems to rest on the claim that turning maths inside-out in this way actually helps to solve some difficult problems in cosmology. Since I have chosen to adopt this system to the very reason that it helps me to solve some difficult problems on the borderlands of cosmology and metaphysics (like the something-from-nothing problem), I wouldn't find it especially surprising if it turned out to be useful for other problems, further over the border in cosmology. The proof of the pudding, in this case, has to be the eating - whether his number system helps to sort out any otherwise intractable cosmological problems (and I can think of several of those).
Geoff
P.S. Cheers for demonstrating that it is possible to question and disagree with someone without feeling the need to treat them as if they were somehow sub-human. Not that difficult, is it?
