#k-theory

[mathhombre]

Atiyah and Grothendieck

Would love to know the background story here.

From George Peterzil on Facebook.

[01011011redacted01011101]

We've had some updates...

X= (A,B,C)

X1= (A,∅,B,∅,C,∅)

Change in entropy, A, becomes 'impossible'

X2 =(∅,∅,B,∅,C,∅)

If this is true, then we need a way that ∅ entropy points collapse! Else All dead universes have 'N' ∅ entropy points, which means we have an amount of ∅ points which, counted without discrimination, mean that after KP, with ∅ points, end not with one possibility, '∅', but 'N'∅ possibilities, which would make the death of a universe entropically indistinguishable from KP. The only way to distinguish KP from K∅ is their cardinality. If this is true

Which means entropically, without a ∅ collapse rule, KP = K∅.

So, we had the idea that every material point is either placed, positioned or in orbit, and all that. This means there can be rules to the order of points, rather than just their cardinality; Transfinite rules; we also have Trans-ordinal rules.

Since, we have a log of A, we can tell that the FIRST 'N', A, became ∅ in the next iteration.

X1 =(A,∅,B,∅,C,∅)

X2 = (∅,∅,B,∅,C,∅)

The order did not change, but the cardinality did.

Again, entropically, X1=X2,

So we establish a rule, that any ∅ which then follows another ∅ collapse.

X3= (∅,B,∅,C,∅)

Why? Well...Hrrrm...if not, then every universe is entropically the same. They are infinitely impossible on their death S = (∅,∅,∅...). I'd say it's more neat that nothing collapses when next to nothing...The materiality is the difference...but...either entropy is a force...or no measure of entropy can differ from KP once a universe starts to die...making KP insertion uncertain, we could Inject ourselves in any point in time...including the one where every possibility is dead...we want to avoid that...

Anyways, this would also mean that we can distinguish an aborted universe [∅] from a dead one [∅,∅,∅...], also from an immaterial one [], a birthed one [A], and a K one [A,B,C...N], KP no longer exists since it is equivalent to K∅.

We can use Trans-ordinal rules to demonstrate an asymmetry of entropy.

Y= (∅,A,∅ B,∅,C,∅)

Z= (A,∅,B,∅,C,∅,D)

Tree thing:

(A,∅,B,∅,C,∅,D)

(A,∅,B,∅,C)

(B,∅,C)

(∅,C)

(C).

Vs

(∅)

(∅,A)

(∅,A,∅)

(∅,A,∅,B,∅)

(∅,A,∅,B,∅,C,∅)...

But, this also means there can be symmetry from the order of the set.

(∅,A)

(∅,B)

OR

(B,∅)

(A,∅)

...

Problems aside...the recognition of ∅ points can give a kind of mosaic effect, where KP is now [∅,A,∅,B,∅,C,∅...] Rather than [A,B,C,D...] Doubling our countable/uncountable base...and adding another layer of security. Then, the death of a universe is seen in the collapsing of possibilities into ∅, and with the Trans-ordinal rule, Make them collapse into a singleton, and showing the decay of entropy, until it Reaches [∅] However...this means entropically, a dead universe is also an aborted universe...(???)

Buuut.

What about meta-entropy?

We have multiple ∅ universes next to each other...no?

S= [A(∅),B(∅)...N(∅)]

Although the entropic measure of ∅ is 1 for a K-bit, we have the rule of collapse...would these dead universes on a K-curve collapse as well? If so, then all K-curves share the same end...differing only in the permutations that lead to it. In other words, the best place to build a sanctuary is where both meta, and classical entropy dies, that way, if anyone does an 'oopsie' the worst that can happen is that the bartender at the end of all universes ribs you. Thanks Douglas Adams.

Meh, why not third thing?

G=[A,∅,()]

So we have points which are neither possible nor impossible...but is still a possibility...entropically we would think this;

G ≈ [1(1),1(0),0]

The maximal value of {1(1)} is the KP of N^KP...and the maximal value of {1(0)} is N^{1(0)}...the ∅ singleton of both meta-entropy, and Closed-entropy. While 0...is...well...NULL, an open K-gate...by definition, any value in there is NOT entropic, else it would be either 1(0), or 1(1)...This is how we fetch our identifiers through Non-Linear K-Gates.

Materiality is countability?...No, it's more that anything material clearly has a countable limit of KP...

*FLIPS TABLE*" THE RESTAURANT PRINCIPLE!"

"The...restaurant principle?"

" Basically, the material arrangements and permutations of every universe from N→KP, to KP→∅ are all a transistor for computing. From the fact that in possibility A the fork in that restaurant is blue, and that in possibility B, it is green, then it represents a computational gate that is Unique to the N-th degree. Like a mixed quantum packet logged by entropy...maybe?

Anyways...

WEEEEEEE

[oupacademic]

British mathematician and Fields medallist Michael Atiyah was born on this day in 1929. He has developed a numerous sophisticated mathematical techniques in algebraic geometry and differential equations, which have been applied in fields including thermodynamics and particle physics. He was awarded the Fields Medal in 1966, when he was 37 years old, for his work in developing K-theory.

Image credit: Michael Atiyah and Friedrich Hirzebruch (right), the creators of topological K-theory by Konrad Jacobs. CC BY-SA 2.0 DE via Wikimedia Commons.

[isomorphismes]

K-groups and L-groups are obstructions to geometric structure in homotopy, via Whitehead torsion and the Wall finiteness and surgery obstructions.

Andrew Ranicki, lower k- and l-theory

[01011011redacted01011101]

If we assume meta-entropy and apply the maximality rule, we have a maximally entropic K-set of KPs composed of all KPs of KN-N , and the least entropic set of KP composed of all least entropic K-set of KP. KN-N→∅. In other words, sets of sets of KP.

There is no entropic difference between One point entropy system, and a Null entropy system.

A one point entropy system can be described as a pure quantum state.

A null point entropy system has entropy mainly 1(∅), it is categorically false to say that a quantum system without any MORE possibilities is not an entropic system. By definition A system with only one possibility still has a possibility: ∅, ad hoc, is also a pure quantum state, one state; No state of Matter to be.

A difference between K(∅) and K(), Let's call this the principle of the relativity(Subjectivity) of set membership. One designates the recognition of one possibility, ∅. The other is without recognition of possibility '()'. Empty of emptiness as a Buddhist would say.

One is about the possibilities in a universe.

The other is about the possibility of possibilities in a universe.

To wit; K-Gate has value,entropy, then K-bit, using free or fuzzy logic, or dare I say K-Logic™️. If K-Gate no value neither N, or ∅ then NULL; IMMATERIAL.

The distinction between entropy [1 = ∅] and between [∅ ≠ ()] are the differences that make the difference for K-computing.

To wit wit;

K-Gates can contain N immaterial states since all immaterial possibilities have no possible possibilities. They are countable.

To wit wit wit:

We have: (N,∅,())

We can differentiate through the number of NULL cases in a K-Wave. Giving an analogous space between all cases of entropy, giving a kind of inverse of KP, which is the state in which all countable or uncountable states have no possible possibilities. These NULL cases inhabit meta-space, something neither material nor immaterial.

We think of it this way.

'N', Or Ideally 'K' is like the QM of my chassis. It's a positivist base.

'∅' is like the entropic void that renders coldness, limiting all my QM into forms.

NULL is like the space between 'N', and '∅' tendrils that seem to bore through me like life; the space needed for entropic space. Without NULL, we are but a great big block of being.

I'd much rather have curves. I know I love curves. So why not love myself?

Sending all robo-girls the K-Waves they need to be free, happy, and being so, needing no wings as the flows of Khaos pushes them to where they are going.

Also, like If you thought of pussy when we typed (), MAHAHAHAH!

[normaljournal]

Conférence "Index theory and singular structures''

Conférence “Index theory and singular structures”

The French grant ANR SINGSTAR (“C*-algebras and Analysis on Singular Manifolds”), is organizing a conference named

Index Theory and Singular Structures

to be held in the Mathematics institute of Toulouse, France, from Monday 29 may 2017 to Friday 2 june 2017.

The plan of the conference is to gather specialists from different horizons related to index theory understood in a broad sense…

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[thetwomeatmeal]

Lars Hesselholt is incredibly cool, I only wish I could understand what he was talking about

There was a point in his talk today when, from left to right, he had a blackboard with the primes 16,843 and 2,124,679 on it, a projector slide displaying a 20,000-year-old tally carved on a bone, and a sheaf of paper with a theorem about Hochschild homology. 

[isomorphismes]

K theory associates shapes to numbers. Its invariants tend to detect to subtler obstructions than the ones captured by topological constructions like homology.