New Math

[mcompengr]

New Math

The big problem for mathematics is that infinity is not a number.

 

In the interest of symmetry, perhaps infinity needs a real partner rather than a clone multiplied by
negative one (-1), infinity far verses small.

 

Infinitiny; Infinitely small, greater than zero, everywhere, a real omnipresence. Its essential quality:
It must be equally as incomprehensible as infinity. Doing away with the numeral '0' does nothing, but zero
has to go. Coordinate axes which do not intersect, perpendicular but separated by some planck-length might
allow that. For computation it could be said that infinity multiplied by infinite small equals one (1).
(Logically okay because this, like infinity, is not a number.) (Infinity x "goes to zero" = 1.) Diverge that.

 

Okay, assuming all fields need a pole, existence and matter fields too: that'd be a discrete-space's 1-membrane.
A regular tetrahedron can be drawn naturally between any two perpendicular, non-intersecting lines like the
x, y-axes above. That "planck-volume" made from four equally spaced points surrounding the 1-brane would be
delineated by six lines, a 6-brane. The real x, y, and z dimensions would then be the three lines through the
center, perpendicular to and bisecting the three pairs of perpendicular lines of the tetrahedron, a 3-brane on
the outside. Ten dimensions then?..

[Acme]

R. Bucky Fuller developed a complex math & geometry by dividing space into tetrahedrons and the tetrahedrons into smaller components that he called quanta modules. Alas the only thing it revealed was what a curious thing is the human imagination. Must be Bucky week as I just referenced Synergetics in another thread on the topic of numerology in base 10.

 

Find both volumes of Synergetics free online here: >> SYNERGETICS: Explorations in the Geometry of Thinking

 

...100.105 All the geometries in the cosmic hierarchy (see Table 982.62) emerge from the successive subdividing of the tetrahedron and its combined parts. After the initial halvings and inadvertent thirdings inherent in the bisecting of the triangles as altogether generated by all seven sets of the great circle equators of symmetrical-systems spin (Sec. 1040), we witness the emergence of:

__ the A quanta modules

__ the octa

__ the "icebergs"

__ the Eighth-Octa

__ the cube

__ the Quarter-Tetra

__ the rhombic dodeca

__ the B quanta modules

__ the icosahedron

__ the T quanta modules

__ the octa-icosa, skewed-off "S" modules

__ the rhombic triacontahedron

__ the E quanta modules

__ the Mites (quarks)

__ the Sytes

__ the Couplers

Edit: Add quote.

Addendum:

New Math

The big problem for mathematics is that ...

This quote seems apropos to the opening point. One does not get any fuller than this.

... 100.62 This moment in the evolutionary advance and psychological transformation of humanity has been held back by non-physically-demonstrable__ergo non- sensorial__conceptionless mathematical devices and by the resultant human incomprehensibility of the findings of science. There are two most prominent reasons for this incomprehensibility: The first is the non-physically demonstrable mathematical tools. The second is our preoccupation with the sense of static, fixed "space" as so much unoccupied geometry imposed by square, cubic, perpendicular, and parallel attempts at coordination, rather than regarding "space" as being merely systemic angle-and-frequency information that is presently non-tuned-in within the physical, sensorial range of tunability of the electromagnetic sensing equipment with which we personally have been organically endowed. ...

Edited October 16, 2014 by Acme

[ajb]

The big problem for mathematics is that infinity is not a number.

I don't think this is exactly a big problem for mathematics, but it does show you have to be careful when formally handling infinities. You might be interested in the notion of the extended real line. In short you append plus and minus infinity to the real numbers. Google it, I am sure you can find more details yourself.

 

Coordinate axes which do not intersect, perpendicular but separated by some planck-length might

allow that.

This is now physics, or maybe noncommutative geometry. I don't see there is some fundamental connection here with the real numbers and infinity.

 

Okay, assuming all fields need a pole, existence and matter fields too...

Again this closer to physics than fundamental mathematics.

[Bignose]

Doing away with the numeral '0' does nothing, but zero

has to go.

With no zero, how am I going to describe how many Lamborghini automobiles I have stored in my garage?

[studiot]

 

With no zero, how am I going to describe how many Lamborghini automobiles I have stored in my garage?

 

 

OOh, can I make a bid of $0.00 (disallowed) for one?

 

Edited October 16, 2014 by studiot

[Delta1212]

With no zero, how am I going to describe how many Lamborghini automobiles I have stored in my garage?

If I'm reading it correctly, and I assume I am despite only skimming about half of it, you would have an infinitesimal number of Lamborghinis.

[Bignose]

If I'm reading it correctly, and I assume I am despite only skimming about half of it, you would have an infinitesimal number of Lamborghinis.

Cool, if I integrate over it, watch out ladies!!!

[mcompengr]

New Math

The big problem for mathematics is that infinity is not a number.

 

In the interest of symmetry, perhaps infinity needs a real partner rather than a clone multiplied by

negative one (-1), infinity far verses small.

 

Infinitiny; Infinitely small, greater than zero, everywhere, a real omnipresence. Its essential quality:

It must be equally as incomprehensible as infinity. Doing away with the numeral '0' does nothing, but zero

has to go. Coordinate axes which do not intersect, perpendicular but separated by some planck-length might

allow that. For computation it could be said that infinity multiplied by infinite small equals one (1).

(Logically okay because this, like infinity, is not a number.) (Infinity x "goes to zero" = 1.) Diverge that.

 

Okay, assuming all fields need a pole, existence and matter fields too: that'd be a discrete-space's 1-membrane.

A regular tetrahedron can be drawn naturally between any two perpendicular, non-intersecting lines like the

x, y-axes above. That "planck-volume" made from four equally spaced points surrounding the 1-brane would be

delineated by six lines, a 6-brane. The real x, y, and z dimensions would then be the three lines through the

center, perpendicular to and bisecting the three pairs of perpendicular lines of the tetrahedron, a 3-brane on

the outside. Ten dimensions then?..

 

The x, y-axes could be log-plotted with variable base and variably scaled from infinity-small to infinity-far (rather than large), with variable alignments and separation allowed. No zero or negative numbers, no addition or subtraction, some other algebra/arithmatic for just exponentiation and any physical number needed from Planckland to Hubbleton. Also, no discontinuities. "Little help" in American Engl. is a request for some of that stuff.

 

Differentiate this: dynamic plotting with equations used to set and control the varying alignment, base and scaling, independently for each axis.

[mcompengr]

With no zero, how am I going to describe how many Lamborghini automobilees I have stored in my garage?

You are all so kind to trust me. We have nothing without that.

Redacted from the complete work: "Counting doesn't count."

[Bignose]

No zero or negative numbers,

Joking about the number of super expensive super cars I own aside, how do you plan on just replacing the apparent presence of negative numbers in nature? Like say the positive and negative charges on ions? Which balance to zero when it is neutral. The current math has been supremely successful at describing this situation. Please demonstrate that your log-based scale can be similar.

[mcompengr]

Joking about the number of super expensive super cars I own aside, how do you plan on just replacing the apparent presence of negative numbers in nature? Like say the positive and negative charges on ions? Which balance to zero when it is neutral. The current math has been supremely successful at describing this situation. Please demonstrate that your log-based scale can be similar.

This would be just another current-math weird-algebra tool, with divergence not possible as the goal.

("new math" means something new under old umbrella) The current math has renormallization which

has no future. Charges are opposite in quality not quantity. Only quantity (counting) is involved in ions

balancing to zero. Can there be opposite quantities the same stuff? With electrons and holes, maybe.

[ajb]

This thread seems to be a mix of random physics words with a little mathematics...

 

So, we are free to construct algebraic structures on sets that have the properties of not having a zero element, that is no identity under a commutative binary operation, which we take to be associative. It seems to me that you will end up with a commutative semigroup. You could dig up A. H. Clifford & G. B. Preston (1964), 'The Algebraic Theory of Semigroups Vol. I' (Second Edition). Semigroups are well studied.

 

Or do you have something else in mind?

[Bignose]

This would be just another current-math weird-algebra tool, with divergence not possible as the goal.

("new math" means something new under old umbrella) The current math has renormallization which

has no future. Charges are opposite in quality not quantity. Only quantity (counting) is involved in ions

balancing to zero. Can there be opposite quantities the same stuff? With electrons and holes, maybe.

So..... No demonstration, then. Just preaching at us that our math has no future. Got it.

 

Until I see a demonstration, I'll stick with what we got. Because I think it has plenty of future. It has certainly been shown to be supremely successful at the moment, and nothing convincing above that it won't be tomorrow, too.

Edited October 18, 2014 by Bignose

[Strange]

Charges are opposite in quality not quantity.

 

In what qualitative way is a negative charge different from a positive charge? That doesn't really make sense; especially as, in many case, charge is relative.

 

 

Can there be opposite quantities the same stuff? With electrons and holes, maybe.

 

I would have said that positrons are much more like the "same stuff" (however you want to define that) than the absence of an electron is. While electron holes do have an effective positive charge, they don't share many other attributes with electrons. Their effective mass is much greater in semiconductors, for example. And I'm not sure, but I have never seen any reference to the spin of holes.

[mcompengr]

 

In what qualitative way is a negative charge different from a positive charge? That doesn't really make sense; especially as, in many case, charge is relative.

 

 

I would have said that positrons are much more like the "same stuff" (however you want to define that) than the absence of an electron is. While electron holes do have an effective positive charge, they don't share many other attributes with electrons. Their effective mass is much greater in semiconductors, for example. And I'm not sure, but I have never seen any reference to the spin of holes.

You are correct: no analogy is perfect, some are awful.

 

Speaking only of charge, are protons and electrons different?

If so, do they differ qualitatively, quantitatively or both?

Charge is being purely quantum, in that none are inside +/- e?

Do you think renormalization (as is) "has a future" so to speak?

 

You dig above now? Trying to lose zero except for counting.

[ajb]

Do you think renormalization (as is) "has a future" so to speak?

There are plenty of people working on renormalisation group methods and so on. I think it will be a subject that stays with us for a while longer yet. Even if a finite theory like string theory is shown to be the correct framework, we will still need effective theories and so renormalisation group techniques will remain.

 

But anyway, this is physics and not mathematics.

 

Trying to lose zero except for counting.

You want to take the set real numbers and remove zero. You can do that for sure. You should then examine what happens with the field axioms. What can you keep without zero and what else has to go. Think about this.

[Strange]

Speaking only of charge, are protons and electrons different?

If so, do they differ qualitatively, quantitatively or both?

 

They are significantly different both quantitatively and qualitatively.

 

Electrons are fundamental particles (fermions) while protons are composite particles (hadrons). Protons are roughly 2,000 times more massive than electrons.

 

Charge is being purely quantum, in that none are inside +/- e?

 

The charge of quarks is +/- 1/3 or 2/3

 

You dig above now?

 

You seem to be mixing up random bits of physics with your mathematics. I don't really understand what you are trying to say.

[ajb]

You seem to be mixing up random bits of physics with your mathematics. I don't really understand what you are trying to say.

I second this statement. We are at a loss as to what you want to do. Understand some algebraic structure without zero (something like an abelian group without the identity), or formulate QFT without renormalisation?