On Tuesday, July 11, 2023 at 11:11:57 PM UTC-7, Ross Finlayson wrote:
On Sunday, July 9, 2023 at 9:56:52 AM UTC-7, Ross Finlayson wrote:
Dana Scott fan club
Been reading some more into Dana Scott. He has a pretty good intuition and is
also a grandiose sort of hedge. Also he knows things and isn't wrong.
Been reading a bit into the Habermas school or Frankfurt school.
Cohen's "Equations from G-d" was a pretty good historical outline about Boole and de Morgan than about Russell about "pure mathematics" in the 19'th century, still though I believe in a stronger platonism and that there's
a science of mathematics but its study is _of_ the real "pure mathematics".
Was reading some Knuth the other day about combinatorics historically, quite a well-rounded guy.Been reading Quine's "Set Theory" (and Quine's number theory and Quine's model theory, ...).
I thought it was pretty good until he got up to real numbers and used the term "non-circularize
the argument" in an off-hand way. He started with a good discussion of class/set distinction
then put it aside and coat-tailed up past "higher-order equals". As a structuralist I don't much
agree except that "equals is first-order", so pretty much the usual coat-tails logician's coat-tailing
of "higher-order equals" comes across as "circularized". So, when Quine got to his real numbers
and was like "my rationals are reals instead of my reals are rationals" then there's a quibble about
least-upper-bound property, pretty much I was disappointed in him when he faked a quibble about
least-upper-bound property. Still, I'm only about half-way through so maybe there will be something
better to talk about later in it.
Dana Scott's pretty good. He's like, "Oh you made an algebra? Here's a boolean lattice."
Reading the other days about Schwarz functions and their distributions and Heaviside's function
and hysteresis and ringing and Gibbs, from some late '90's papers from NASA, about doubling-spaces
and the non-standard and infinitesimals, I figure that it still makes pretty great sense the re-Vitali-ization
of measure theory ("after LUB, the other axiom, measure 1.0"), into doubling spaces and Ramsey theory,
figuring they'll need a foundations besides their applied.
The stopping-derivative is kind of an interesting idea, I've been thinking about the identity dimension
and a bunch of great stuff that arrives from re-Vitali-ization and a deconstructive account of the
arithmetic and so on.
Well I kept reading Quine's book on set theory, "Set Theory ...", and it's really pretty great
and one of the better or the best overall books on set theory.
He goes on to explain the various perspectives and approaches to the objects of set theory,
elements have memberships (elt, set theory, Mengen),
classes have members (contains, part theory, Unmenge),
and explains various organizations of primary objects
Frege and his numbers,
von Neumann and about functions,
Russell with types,
Zermelo and well-foundings
and about well-orderings and ordering theory.
What I notice of it is as the various concerns of the concepts of the objects,
circle about a common drain,
set and part theory,
ordering theory,
number theory,
function theory
so this sits very well with my approaches to ubiquitous ordinals,
topology and function theory making for geometry, that to make
for a circularizing of the circularizing, has that pretty much I can mark the salient points in Quine that have where these approaches define
each other in terms of each other, and suss out a unified approach to them-all.
When it comes to coat-tails, here it's canonry, where fully I intend that it's one giant coat-tails. (And none.)
For foundations, it's a foundations of logical objects, mathematical objects,
all one theory.
Yeah, I'm pretty happy I wrote an apologetics for modern mathematics and paleo-classical post-modern extra-standard ubiquitous ordinals in primary objects and ur-elements after all universal theory.
Don't need another one, ....
Quine shirt-sleeves quite a few good quotes on the topic.
OpenAI will not buy chips from Iran. Rather Korea.
Sam Altman, co-founder and CEO of OpenAI --the tech company
that wowed the world with the release of generative AI platform
ChatGPT --visited Seoul last week as part of the "OpenAI Tour 2023."
For an in-depth analysis, we invited Lee Soo-young, professor
emeritus at KAIST. We also have Ashique KhudaBukhsh, a professor
at the Rochester Institute of Technology. Arirang News.
OpenAI Chief Sam Altman meets Pres. Yoon and
says S. Korea should focus on chips https://www.youtube.com/watch?v=WruSvgjRCX0
Ross Finlayson schrieb am Montag, 26. Juni 2023 um 06:40:26 UTC+2:
On Friday, June 23, 2023 at 1:50:56 AM UTC-7, Mild Shock wrote:
If its embarrassingly parallel you can scale easily.
But what about the FPGA qubits. The article writes:
"In the latter paper, which includes a great overview of
the state of the art, Pilch and colleagues summarize
this as shifting the processing from time to space —
from using slow sequential CPU processing to hardware
complexity, using the FPGA’s configurable fabric
and inherent parallelism."
- in reference to FPGA emulation of quantum
circuits, A.U. Khalid et al.
Jeff Barnett schrieb am Freitag, 23. Juni 2023 um 09:32:24 UTC+2:
On 6/23/2023 1:10 AM, Mild Shock wrote:
Not only the speed doesn't double every year anymore, also the number
of transistors doesn't double every year anymore. See also:
‘Moore’s Law’s dead,’ Nvidia CEO https://www.marketwatch.com/story/moores-laws-dead-nvidia-ceo-jensen-says-in-justifying-gaming-card-price-hike-11663798618
Does the FPGA qubits idea some benefit in this respect?
Mild Shock schrieb am Dienstag, 20. Juni 2023 um 17:11:59 UTC+2:I think Moore's observation was that the *density* of components approximately double about ever 2 years. He didn't mention speed; that's
To hell with GPUs. Here come the FPGA qubits:
Iran’s Military Quantum Claim: It’s Only 99.4% Ridiculous
https://hackaday.com/2023/06/15/irans-quantum-computing-on-fpga-claim-its-kinda-a-thing/
The superposition property enables a quantum computer
to be in multiple states at once.
https://www.techtarget.com/whatis/definition/qubit
Maybe their new board is even less suited for hitting
a ship with a torpedo than some machine learning?
a belief commonly ascribed to Moore however. I just took a peek at a chart in a Wikipedia article from way back when up to 2020 or so. The prediction still seemed to have some support.
In fact the idea that speed will continue its exponential rise with the
passing of time must be better quantified in order to judge what's going
on. The trick in the chip industry is to supply more and more cores in the same amount of real estate with modest (if any) speed gains.
Something like a "surface acoustic wave transducer" is what lots of plain ordinaryIf n cores could do n times as much computation per unit time as a single core, we would have Moore's Corollary "speed doubles approximately every two years." As we all know from bitter experience, that linear relation between number of cores and speed of computation is
a pipe dream for most computation classes. For those classes where such
a speed up can be realized, the complexity of the programing to achieve
it is too high for most of us.
--
Jeff Barnett
linked parallel gate arrays employ something like Maugin's mathematics of the
non-linear or mostly about implicits and parameterizations of the piezoelectric
and models of acoustic waves in silico, it's not really "quantum computing"
any more than "simulated annealing" solves non-linear equations. (Cf. "D-Wave".)
It's massive wide parallel.
Ok, OpenAI is dead. But we need to get out of the claws
of the computing cloud. We need the spirit of Niklaus
Wirth, who combined computer science and
electronics. We need to solve the problem of
parallel slilicon. Should have a look again at these
quantum computers. Can we have them on the Edge?
Mild Shock schrieb am Montag, 10. Juli 2023 um 18:46:12 UTC+2:
OpenAI will not buy chips from Iran. Rather Korea.
Sam Altman, co-founder and CEO of OpenAI --the tech company
that wowed the world with the release of generative AI platform
ChatGPT --visited Seoul last week as part of the "OpenAI Tour 2023."
For an in-depth analysis, we invited Lee Soo-young, professor
emeritus at KAIST. We also have Ashique KhudaBukhsh, a professor
at the Rochester Institute of Technology. Arirang News.
OpenAI Chief Sam Altman meets Pres. Yoon and
says S. Korea should focus on chips https://www.youtube.com/watch?v=WruSvgjRCX0
Ross Finlayson schrieb am Montag, 26. Juni 2023 um 06:40:26 UTC+2:
On Friday, June 23, 2023 at 1:50:56 AM UTC-7, Mild Shock wrote:
If its embarrassingly parallel you can scale easily.
But what about the FPGA qubits. The article writes:
"In the latter paper, which includes a great overview of
the state of the art, Pilch and colleagues summarize
this as shifting the processing from time to space —
from using slow sequential CPU processing to hardware
complexity, using the FPGA’s configurable fabric
and inherent parallelism."
- in reference to FPGA emulation of quantum
circuits, A.U. Khalid et al.
Jeff Barnett schrieb am Freitag, 23. Juni 2023 um 09:32:24 UTC+2:
On 6/23/2023 1:10 AM, Mild Shock wrote:
Not only the speed doesn't double every year anymore, also the number
of transistors doesn't double every year anymore. See also:
‘Moore’s Law’s dead,’ Nvidia CEO https://www.marketwatch.com/story/moores-laws-dead-nvidia-ceo-jensen-says-in-justifying-gaming-card-price-hike-11663798618
Does the FPGA qubits idea some benefit in this respect?
Mild Shock schrieb am Dienstag, 20. Juni 2023 um 17:11:59 UTC+2:I think Moore's observation was that the *density* of components approximately double about ever 2 years. He didn't mention speed; that's
To hell with GPUs. Here come the FPGA qubits:
Iran’s Military Quantum Claim: It’s Only 99.4% Ridiculous
https://hackaday.com/2023/06/15/irans-quantum-computing-on-fpga-claim-its-kinda-a-thing/
The superposition property enables a quantum computer
to be in multiple states at once.
https://www.techtarget.com/whatis/definition/qubit
Maybe their new board is even less suited for hitting
a ship with a torpedo than some machine learning?
a belief commonly ascribed to Moore however. I just took a peek at a chart in a Wikipedia article from way back when up to 2020 or so. The
prediction still seemed to have some support.
In fact the idea that speed will continue its exponential rise with the
passing of time must be better quantified in order to judge what's going
on. The trick in the chip industry is to supply more and more cores in
the same amount of real estate with modest (if any) speed gains.
Something like a "surface acoustic wave transducer" is what lots of plain ordinaryIf n cores could do n times as much computation per unit time as a single core, we would have Moore's Corollary "speed doubles approximately every two years." As we all know from bitter experience,
that linear relation between number of cores and speed of computation is
a pipe dream for most computation classes. For those classes where such
a speed up can be realized, the complexity of the programing to achieve
it is too high for most of us.
--
Jeff Barnett
linked parallel gate arrays employ something like Maugin's mathematics of the
non-linear or mostly about implicits and parameterizations of the piezoelectric
and models of acoustic waves in silico, it's not really "quantum computing"
any more than "simulated annealing" solves non-linear equations. (Cf. "D-Wave".)
It's massive wide parallel.
On Thursday, July 13, 2023 at 11:51:10 PM UTC-7, Ross Finlayson wrote:
On Tuesday, July 11, 2023 at 11:11:57 PM UTC-7, Ross Finlayson wrote:
On Sunday, July 9, 2023 at 9:56:52 AM UTC-7, Ross Finlayson wrote:
Dana Scott fan club
Been reading some more into Dana Scott. He has a pretty good intuition and is
also a grandiose sort of hedge. Also he knows things and isn't wrong.
Been reading a bit into the Habermas school or Frankfurt school.
Cohen's "Equations from G-d" was a pretty good historical outline about
Boole and de Morgan than about Russell about "pure mathematics" in the 19'th century, still though I believe in a stronger platonism and that there's
a science of mathematics but its study is _of_ the real "pure mathematics".
Was reading some Knuth the other day about combinatorics historically, quite a well-rounded guy.Been reading Quine's "Set Theory" (and Quine's number theory and Quine's model theory, ...).
I thought it was pretty good until he got up to real numbers and used the term "non-circularize
the argument" in an off-hand way. He started with a good discussion of class/set distinction
then put it aside and coat-tailed up past "higher-order equals". As a structuralist I don't much
agree except that "equals is first-order", so pretty much the usual coat-tails logician's coat-tailing
of "higher-order equals" comes across as "circularized". So, when Quine got to his real numbers
and was like "my rationals are reals instead of my reals are rationals" then there's a quibble about
least-upper-bound property, pretty much I was disappointed in him when he faked a quibble about
least-upper-bound property. Still, I'm only about half-way through so maybe there will be something
better to talk about later in it.
Dana Scott's pretty good. He's like, "Oh you made an algebra? Here's a boolean lattice."
Reading the other days about Schwarz functions and their distributions and Heaviside's function
and hysteresis and ringing and Gibbs, from some late '90's papers from NASA, about doubling-spaces
and the non-standard and infinitesimals, I figure that it still makes pretty great sense the re-Vitali-ization
of measure theory ("after LUB, the other axiom, measure 1.0"), into doubling spaces and Ramsey theory,
figuring they'll need a foundations besides their applied.
The stopping-derivative is kind of an interesting idea, I've been thinking about the identity dimension
and a bunch of great stuff that arrives from re-Vitali-ization and a deconstructive account of the
arithmetic and so on.
Well I kept reading Quine's book on set theory, "Set Theory ...", and it's really pretty great
and one of the better or the best overall books on set theory.
He goes on to explain the various perspectives and approaches to the objects of set theory,
elements have memberships (elt, set theory, Mengen),
classes have members (contains, part theory, Unmenge),
and explains various organizations of primary objects
Frege and his numbers,
von Neumann and about functions,
Russell with types,
Zermelo and well-foundings
and about well-orderings and ordering theory.
What I notice of it is as the various concerns of the concepts of the objects,
circle about a common drain,
set and part theory,
ordering theory,
number theory,
function theory
so this sits very well with my approaches to ubiquitous ordinals,
topology and function theory making for geometry, that to make
for a circularizing of the circularizing, has that pretty much I can mark the salient points in Quine that have where these approaches define
each other in terms of each other, and suss out a unified approach to them-all.
When it comes to coat-tails, here it's canonry, where fully I intend that it's one giant coat-tails. (And none.)
For foundations, it's a foundations of logical objects, mathematical objects,
all one theory.
Yeah, I'm pretty happy I wrote an apologetics for modern mathematics and paleo-classical post-modern extra-standard ubiquitous ordinals in primary objects and ur-elements after all universal theory.
Don't need another one, ....
Quine shirt-sleeves quite a few good quotes on the topic.
Here's an example of a 2023 paper about continuous domains that references a Scott topology.
https://arxiv.org/abs/2301.09940
It sort of makes you wonder how such a, "countable continuous domain", could be, without tipping each other's carts.
"In the infinitary logic", ....
It's funny if you search for "countable continuous domain" nothing shows up, but "modern foundations" "set theory"
"countable continuous domain" sort of arrives here.
On Sunday, November 19, 2023 at 6:44:08 PM UTC-8, Ross Finlayson wrote:
On Thursday, July 13, 2023 at 11:51:10 PM UTC-7, Ross Finlayson wrote:
On Tuesday, July 11, 2023 at 11:11:57 PM UTC-7, Ross Finlayson wrote:
On Sunday, July 9, 2023 at 9:56:52 AM UTC-7, Ross Finlayson wrote:
Dana Scott fan club
Been reading some more into Dana Scott. He has a pretty good intuition and is
also a grandiose sort of hedge. Also he knows things and isn't wrong.
Been reading a bit into the Habermas school or Frankfurt school.
Cohen's "Equations from G-d" was a pretty good historical outline about
Boole and de Morgan than about Russell about "pure mathematics" in the
19'th century, still though I believe in a stronger platonism and that there's
a science of mathematics but its study is _of_ the real "pure mathematics".
Was reading some Knuth the other day about combinatorics historically,Been reading Quine's "Set Theory" (and Quine's number theory and Quine's model theory, ...).
quite a well-rounded guy.
I thought it was pretty good until he got up to real numbers and used the term "non-circularize
the argument" in an off-hand way. He started with a good discussion of class/set distinction
then put it aside and coat-tailed up past "higher-order equals". As a structuralist I don't much
agree except that "equals is first-order", so pretty much the usual coat-tails logician's coat-tailing
of "higher-order equals" comes across as "circularized". So, when Quine got to his real numbers
and was like "my rationals are reals instead of my reals are rationals" then there's a quibble about
least-upper-bound property, pretty much I was disappointed in him when he faked a quibble about
least-upper-bound property. Still, I'm only about half-way through so maybe there will be something
better to talk about later in it.
Dana Scott's pretty good. He's like, "Oh you made an algebra? Here's a boolean lattice."
Reading the other days about Schwarz functions and their distributions and Heaviside's function
and hysteresis and ringing and Gibbs, from some late '90's papers from NASA, about doubling-spaces
and the non-standard and infinitesimals, I figure that it still makes pretty great sense the re-Vitali-ization
of measure theory ("after LUB, the other axiom, measure 1.0"), into doubling spaces and Ramsey theory,
figuring they'll need a foundations besides their applied.
The stopping-derivative is kind of an interesting idea, I've been thinking about the identity dimension
and a bunch of great stuff that arrives from re-Vitali-ization and a deconstructive account of the
arithmetic and so on.
Well I kept reading Quine's book on set theory, "Set Theory ...", and it's really pretty great
and one of the better or the best overall books on set theory.
He goes on to explain the various perspectives and approaches to the objects of set theory,
elements have memberships (elt, set theory, Mengen),
classes have members (contains, part theory, Unmenge),
and explains various organizations of primary objects
Frege and his numbers,
von Neumann and about functions,
Russell with types,
Zermelo and well-foundings
and about well-orderings and ordering theory.
What I notice of it is as the various concerns of the concepts of the objects,
circle about a common drain,
set and part theory,
ordering theory,
number theory,
function theory
so this sits very well with my approaches to ubiquitous ordinals, topology and function theory making for geometry, that to make
for a circularizing of the circularizing, has that pretty much I can mark
the salient points in Quine that have where these approaches define
each other in terms of each other, and suss out a unified approach to them-all.
When it comes to coat-tails, here it's canonry, where fully I intend that
it's one giant coat-tails. (And none.)
For foundations, it's a foundations of logical objects, mathematical objects,
all one theory.
Yeah, I'm pretty happy I wrote an apologetics for modern mathematics and paleo-classical post-modern extra-standard ubiquitous ordinals in primary
objects and ur-elements after all universal theory.
Don't need another one, ....
Quine shirt-sleeves quite a few good quotes on the topic.
Here's an example of a 2023 paper about continuous domains that references a Scott topology.
https://arxiv.org/abs/2301.09940
It sort of makes you wonder how such a, "countable continuous domain", could be, without tipping each other's carts.
"In the infinitary logic", ....
It's funny if you search for "countable continuous domain" nothing shows up, but "modern foundations" "set theory"If you're interested in some of Scott's examples of topologies and topologies via logic, you might appreciate Vickers' "Topology via Logic".
"countable continuous domain" sort of arrives here.
The usual open topology of course and zero being rational gets into
why otherwise for example rationals and irrationals would be indistinguishable
except for their countability. "Topology via Logic" introduces others.
This Hofmann-Mislove theorem also sort of provides a complement/alternative, to something like Dedekind completeness, if you don't not look the other way.
Then, one might aver that this leads to contradictions unless there's some way
to model various sorts of continuous domains, like line/field/signal reals.
On Tuesday, August 22, 2023 at 7:57:56 PM UTC-7, Dan Christensen wrote:there are times when one has to distinguish between the two. For instance, if f : R → R is the function f(x) := x2, and g := f|[1,2] is the restriction of f to the interval [1, 2], then f and g both perform the operation of squaring, i.e., f(x) = x^2
On Tuesday, August 22, 2023 at 10:09:38 PM UTC-4, Ben Bacarisse wrote:
Dan Christensen <[email protected]> writes:Some context:
On Tuesday, August 22, 2023 at 7:01:09 PM UTC-4, Fritz Feldhase wrote: >>>>> On Tuesday, August 22, 2023 at 8:01:09 PM UTC+2, Dan Christensen wrote: >>>>>Tao does not support your claim. For example (from the same book):
Functions f and g are comparable only if they have the same domain >>>>>> and codomain.
Anyone except crank DC knows that this is nonsense.
"Definition 3.3.7 (Equality of functions). Two functions f : X → Y , >>>> g : X → Y with the same domain and range [codomain] are said to be equal, f = g,
if and only if f(x) = g(x) for all x ∈ X. "
---Terence Tao, "Analysis I," p.51 (Perhaps you have heard of him?)
"... the two functions f and g are not considered the same function,
f =/= g, because they have different domains."
"Strictly speaking, there is a distinction between a function f, and its value f(x) at a point x. f is a function; but f(x) is a number (which depends on some free variable x). This distinction is rather subtle and we will not stress it too much, but
--p. 218
It would disingenuous to suggest that this discussion of liberties often taken in the literature is somehow a repudiation of his formal definition of the equality of functions. "[W]e shall often be careless, and say things like..."
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Function theory is among the most overloaded of the fields of elementary kinds of objects,
over time.
It's as of matters of relations, where relations are about being more fundamental than predicates,
even though usually enough it's the other way way. Other usual examples includes integers
then rationals or integers in rationals, where intensionality and extensionality get reversible
because they are reversible because there's a geometry of points and spaces for the most of
the assignments of the mathematical objects and it's reversible.
Now, coming from a guy like Dan who says "I proved 0^0 = 1", and it's like no you didn't, you
picked a branch of a multiplicity as what was a singularity to make a regularity and your
restriction of comprehension is noted as simply a letting, to "let", something be, that's
otherwise it's just another usual sort of wishful thinking. Because, for example, otherwise
you'd accept there aren't negative numbers, there aren't complex numbers, and so on,
just like other usual retro-finitist trolls of the sourpuss, folderol, and jibing ape variety.
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