The British Sunday newspaper referred to in the Reuters report is the Observer, and their story, which has a few more details and some funny bits, is
here.
This guy re-installed Redhat because he couldn't manage to install new KDE 2.2 packages. And he takes it out on "Linux," when he should of course take it out on Redhat. I know I updated KDE with a few commands involving urpmi on my Mandrake install, and it should be even simpler to do on Debian -- certainly much simpler than upgrading something equivalent on MS Windows.
He may be "taking it out" on Redhat, but it needs to be appreciated that the many-name issue is confusing to the newcomer. I remember coming to Linux a couple of years ago and being pretty confused about the different levels and names branded across the system: Linux, X windows, Red Hat, Gnome, Helix, Enlightenment. What are all these things? What do they do? What's the difference? I know the answers now (except that I'm still pretty confused about what exactly X does), but it's daunting to a newbie - even one technically-minded enough to end up reading Slashdot.
Strictly speaking, the property mentioned isn't actually normality, but normality to base 10^n for all n. Normality to base b means that if you write down the base-b expression for the number then every base-b digit occurs with equal frequency. So normality to base 10 means that in the usual decimal expansion, 3 and 7 occur with equal frequency, for instance. Normality to base 100 means that, e.g., in the decimal expansion 34 and 87 occur with equal frequency.
It's known that in a certain precise sense, almost all numbers are normal (i.e. normal to *all* bases). But to this day, not one single specific number has been *proved* to be normal!
The Guardian, a left-leaning British newspaper, has had just two stories on Sklyarov (as far as I can see). One of them is
here.
This will probably tell Slashdot readers nothing new, but the journalist's
own page
has various interesting Sklyarov links, including to the Powerpoint file of his Defcon presentation.
As a full-time mathematician I'm half-pleased to see the existence of this project, but I'm not really very thrilled with it. It's the big concepts that attract me to maths, the ideas and the big picture, not the nitty-gritty of putting together lots of little logical steps. So as a matter of taste, I don't think that Metamath presents a very appealing view of maths, and I suspect that some people will be actively put off maths by this. If not then fine, but this is my personal feeling.
Another reservation I have about this is its concentration on axiomatic set theory. This is a subject which tends to draw a lot of attention from the non-mathematics community, in popular science books and so on. In fact it's quite far out of the mainstream of mathematics (a sociological observation rather than a value judgement). I think that the importance of set theory as a "foundation" and "universal language" for mathematics has been far overstated.
This point of view on set theory is actually increasingly prevalent among the theoretical computer science community - at least, the part of it that I come into contact with. There are various structures from mathematical logic that are far more applicable to computer science than sets are: for instance, the lambda-calculus and categories. Metamath is very reductionist in its approach: it takes the smallest building blocks and shows in minute detail how they can be put together to obtain familiar objects. In contrast, the more popular modern approach is to try and describe things from the top down, e.g. one might look for abstract mathematical structures which resemble the collection of datatypes in a particular programming language.
So it's kind of nice to see this here, but it's not the face of mathematics I'd choose to present.
...and a couple more chunks are here, for your reading delight. Most of the article makes heavy use of figures so wouldn't be much use posted here.
Materials and Methods
Fabrication of Microfluidic System. Our method for the fabrication of a 3D microfluidic system has been described in detail elsewhere
(refs. 13 and 14). Briefly, the silicon master was fabricated by first spinning a negative photoresist (SU 8-50 or SU 8-100) onto a silicon
wafer, which has been cleaned by sonicating in acetone (5 min) then in methanol (5 min) and dried by baking at 180C (10 min). The
photoresist-covered wafer was soft baked (105C for 15 min) to evaporate the solvent, let cool, then placed under a photomask in a Karl
Suss mask-aligner (Zeiss) to expose the photoresist. The exposed photoresist was baked (105C for 5 min), then developed in propylene
glycol methyl ether acetate to create a master with one level of feature. Masters with two levels of feature were fabricated by repeating
this procedure with a different photomask. The masters were silanized in vacuo (in a desiccator) with 0.5 ml tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichloros ilane
for 12 h. The silanized masters were then used for molding slabs and membranes of poly(dimethylsiloxane) (PDMS). To fabricate the PDMS membrane, a drop of
PDMS prepolymer was sandwiched between the master and a Teflon sheet and was allowed to cure overnight under pressure (10-50 kPa) at 70C. The cured PDMS
membranes and slabs were aligned by using a home-built micromanipulator stage, oxidized in a plasma cleaner (model SP100 Plasma System, Anatech, Alexandria,
VA) for 40 sec at 60 W under [roughly equal to] 0.2 Torr (1 torr = 133 Pa) oxygen, and brought into contact to form an irreversible seal. This procedure of alignment, oxidation, and
sealing was repeated multiple times for the fabrication of a multilayer microfluidic system.
Chemicals. Negative photoresists (SU 8-50 and SU 8-100) were obtained from Microlithography Chemical (Newton, MA), propylene glycol methyl ether acetate
from Aldrich, tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichloros ilane from United Chemical Technologies (Bristol, PA), PDMS prepolymer (Sylgard 184) from
Dow-Corning, fluorescent nanospheres from Molecular Probes, and silicon wafers from Silicon Sense (Nashua, NH).
[...]
Conclusions
The strength of this microfluidic system as an analog computational device is its high parallelism. Its weakness is the exponential increase
in its physical size with the number of vertices. This space-time tradeoff is reminiscent of the limitations of using DNA for solving large
NP problems (refs. 5-7). We estimate that the largest graph that might be solved with our algorithmby using 12-inch wafers
(commercially available) and 200-nm channels (within the range of photolithography)is 20 vertices. If we use space more efficiently
by encoding subgraphs in a plane and use the third dimension for fluid flow, we might solve 40-vertex graphs. By using a computer
capable of performing 109 operations per second, a 40-vertex graph can be solved in about 20 min, which makes this microfluidic
approach (in its current form) impractical to compete with traditional silicon computers for solving large search problems. In comparison to DNA-based computation,
this microfluidic system can carry out certain logical operations, such as addition, more naturally. The z-direction flow in the four-layer microfluidic device (Fig. 4) acts
as an integrator by adding the beads that arrive at the wells from all of the layers. In contrast, the implementation of an algorithm for DNA-based addition was
nontrivial (ref. 8), although a far more direct method for DNA addition has been proposed (ref. 17) and partially implemented (ref. 18).
The algorithm we described here for using fluids to search the parallel architecture of a microfluidic system could also, perhaps, be implemented in a 3D
microelectronic circuit. There are, however, several advantages to using microfluidic systems. (i) Fluids can carry fluorescent beads or molecules, thereby making the
readout by using parallel optical systems simpler than in microelectronic circuits. (ii) Many different "color" beads/molecules can be used in microfluidic systems,
whereas electrons have only one "color"; this feature permits fluidic systems to encode more information than electrical systems. (iii) Microfluidic systems might not
require power (our algorithm, for example, can be implemented by using gravity). Advantages of electrical over fluidic systems include ease of use (no clogging of
channels) and the high speed at which electrons travel through the circuit (which is important for implementing sequential algorithms). Although clogging is a concern
in microfluidic systems, it was not a problem under our experimental conditions, because of the relatively small sizes of the beads used (400 nm or smaller) compared
with the widths of the microchannels (50 m or greater).
Another motivation for using microfluidic-based computation is the possibility of integrating fluidic components for controlling complex chip-based microanalytical
devices. In addition, computation by using microfluidic systems are complementary to ones based on biological molecules (e.g., DNA) or coupled chemical reactions
(refs. 19 and 20). The wells and channels in our 3D microfluidic system, for example, could compartmentalize and transport molecules and reactions for the
construction of a chemical or DNA-based computer.
Slashdot Mirror
The British Sunday newspaper referred to in the Reuters report is the Observer, and their story, which has a few more details and some funny bits, is here.
He may be "taking it out" on Redhat
Bah, I meant Linux, not Redhat. Obviously I'm still as confused as ever
This guy re-installed Redhat because he couldn't manage to install new KDE 2.2 packages. And he takes it out on "Linux," when he should of course take it out on Redhat. I know I updated KDE with a few commands involving urpmi on my Mandrake install, and it should be even simpler to do on Debian -- certainly much simpler than upgrading something equivalent on MS Windows.
He may be "taking it out" on Redhat, but it needs to be appreciated that the many-name issue is confusing to the newcomer. I remember coming to Linux a couple of years ago and being pretty confused about the different levels and names branded across the system: Linux, X windows, Red Hat, Gnome, Helix, Enlightenment. What are all these things? What do they do? What's the difference? I know the answers now (except that I'm still pretty confused about what exactly X does), but it's daunting to a newbie - even one technically-minded enough to end up reading Slashdot.Strictly speaking, the property mentioned isn't actually normality, but normality to base 10^n for all n. Normality to base b means that if you write down the base-b expression for the number then every base-b digit occurs with equal frequency. So normality to base 10 means that in the usual decimal expansion, 3 and 7 occur with equal frequency, for instance. Normality to base 100 means that, e.g., in the decimal expansion 34 and 87 occur with equal frequency.
It's known that in a certain precise sense, almost all numbers are normal (i.e. normal to *all* bases). But to this day, not one single specific number has been *proved* to be normal!
The Guardian, a left-leaning British newspaper, has had just two stories on Sklyarov (as far as I can see). One of them is here. This will probably tell Slashdot readers nothing new, but the journalist's own page has various interesting Sklyarov links, including to the Powerpoint file of his Defcon presentation.
As a full-time mathematician I'm half-pleased to see the existence of this project, but I'm not really very thrilled with it. It's the big concepts that attract me to maths, the ideas and the big picture, not the nitty-gritty of putting together lots of little logical steps. So as a matter of taste, I don't think that Metamath presents a very appealing view of maths, and I suspect that some people will be actively put off maths by this. If not then fine, but this is my personal feeling.
Another reservation I have about this is its concentration on axiomatic set theory. This is a subject which tends to draw a lot of attention from the non-mathematics community, in popular science books and so on. In fact it's quite far out of the mainstream of mathematics (a sociological observation rather than a value judgement). I think that the importance of set theory as a "foundation" and "universal language" for mathematics has been far overstated.
This point of view on set theory is actually increasingly prevalent among the theoretical computer science community - at least, the part of it that I come into contact with. There are various structures from mathematical logic that are far more applicable to computer science than sets are: for instance, the lambda-calculus and categories. Metamath is very reductionist in its approach: it takes the smallest building blocks and shows in minute detail how they can be put together to obtain familiar objects. In contrast, the more popular modern approach is to try and describe things from the top down, e.g. one might look for abstract mathematical structures which resemble the collection of datatypes in a particular programming language.
So it's kind of nice to see this here, but it's not the face of mathematics I'd choose to present.
Materials and Methods
Fabrication of Microfluidic System. Our method for the fabrication of a 3D microfluidic system has been described in detail elsewhere (refs. 13 and 14). Briefly, the silicon master was fabricated by first spinning a negative photoresist (SU 8-50 or SU 8-100) onto a silicon wafer, which has been cleaned by sonicating in acetone (5 min) then in methanol (5 min) and dried by baking at 180C (10 min). The photoresist-covered wafer was soft baked (105C for 15 min) to evaporate the solvent, let cool, then placed under a photomask in a Karl Suss mask-aligner (Zeiss) to expose the photoresist. The exposed photoresist was baked (105C for 5 min), then developed in propylene glycol methyl ether acetate to create a master with one level of feature. Masters with two levels of feature were fabricated by repeating this procedure with a different photomask. The masters were silanized in vacuo (in a desiccator) with 0.5 ml tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichloros ilane
for 12 h. The silanized masters were then used for molding slabs and membranes of poly(dimethylsiloxane) (PDMS). To fabricate the PDMS membrane, a drop of
PDMS prepolymer was sandwiched between the master and a Teflon sheet and was allowed to cure overnight under pressure (10-50 kPa) at 70C. The cured PDMS
membranes and slabs were aligned by using a home-built micromanipulator stage, oxidized in a plasma cleaner (model SP100 Plasma System, Anatech, Alexandria,
VA) for 40 sec at 60 W under [roughly equal to] 0.2 Torr (1 torr = 133 Pa) oxygen, and brought into contact to form an irreversible seal. This procedure of alignment, oxidation, and
sealing was repeated multiple times for the fabrication of a multilayer microfluidic system.
Chemicals. Negative photoresists (SU 8-50 and SU 8-100) were obtained from Microlithography Chemical (Newton, MA), propylene glycol methyl ether acetate from Aldrich, tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichloros ilane from United Chemical Technologies (Bristol, PA), PDMS prepolymer (Sylgard 184) from
Dow-Corning, fluorescent nanospheres from Molecular Probes, and silicon wafers from Silicon Sense (Nashua, NH).
[...]
Conclusions
The strength of this microfluidic system as an analog computational device is its high parallelism. Its weakness is the exponential increase in its physical size with the number of vertices. This space-time tradeoff is reminiscent of the limitations of using DNA for solving large NP problems (refs. 5-7). We estimate that the largest graph that might be solved with our algorithmby using 12-inch wafers (commercially available) and 200-nm channels (within the range of photolithography)is 20 vertices. If we use space more efficiently by encoding subgraphs in a plane and use the third dimension for fluid flow, we might solve 40-vertex graphs. By using a computer capable of performing 109 operations per second, a 40-vertex graph can be solved in about 20 min, which makes this microfluidic approach (in its current form) impractical to compete with traditional silicon computers for solving large search problems. In comparison to DNA-based computation, this microfluidic system can carry out certain logical operations, such as addition, more naturally. The z-direction flow in the four-layer microfluidic device (Fig. 4) acts as an integrator by adding the beads that arrive at the wells from all of the layers. In contrast, the implementation of an algorithm for DNA-based addition was nontrivial (ref. 8), although a far more direct method for DNA addition has been proposed (ref. 17) and partially implemented (ref. 18).
The algorithm we described here for using fluids to search the parallel architecture of a microfluidic system could also, perhaps, be implemented in a 3D microelectronic circuit. There are, however, several advantages to using microfluidic systems. (i) Fluids can carry fluorescent beads or molecules, thereby making the readout by using parallel optical systems simpler than in microelectronic circuits. (ii) Many different "color" beads/molecules can be used in microfluidic systems, whereas electrons have only one "color"; this feature permits fluidic systems to encode more information than electrical systems. (iii) Microfluidic systems might not require power (our algorithm, for example, can be implemented by using gravity). Advantages of electrical over fluidic systems include ease of use (no clogging of channels) and the high speed at which electrons travel through the circuit (which is important for implementing sequential algorithms). Although clogging is a concern in microfluidic systems, it was not a problem under our experimental conditions, because of the relatively small sizes of the beads used (400 nm or smaller) compared with the widths of the microchannels (50 m or greater).
Another motivation for using microfluidic-based computation is the possibility of integrating fluidic components for controlling complex chip-based microanalytical devices. In addition, computation by using microfluidic systems are complementary to ones based on biological molecules (e.g., DNA) or coupled chemical reactions (refs. 19 and 20). The wells and channels in our 3D microfluidic system, for example, could compartmentalize and transport molecules and reactions for the construction of a chemical or DNA-based computer.
Well, the more competition the better: it increases the chances of a good free-of-charge updating service. BTW, Happy Birthday ctsnydal.