Let $R$ be a symmetric relation on set $S$ of length $n$. Let $b \in S$ and let $\beta_b = \{a | b R a \wedge a \neq b\}$. Let $k(b)=|\beta_b|$ be the cardinality of $b$.
Theorem:
$\exists a,b \in S : k(a) = k(b)$
Proof:
Assume there doesn't exist such a and b. Then all our elements in $S$ has different cardinalities. We have $n$ elements so we need $n$ different cardinalities. Maximum cardinality possible is $n-1$. So our cardinalities range from $0$ to $n-1$. If there is element $y$ whose cardinality $n-1$ then $\exists_{n-1} a : y R a$, i.e. all other elements than $y$ has cardinality $\geq 1$. Hence there is no element with cardinality $0$. And then we don't have $n$ different cardinalities, contradiction. The theorem holds $\qed$
Monday, December 21, 2009
Sunday, December 6, 2009
Universal services
I have moved my favorite album sharing service from facebook to picasaweb.
Picasaweb has several advantages over facebook from my point of view. The most important one is the ability to store images with original quality. Auto-tagging is also a great relief, that you can tag faces of people much much faster. Also, for shared events all people can upload to one common album, unlike facebook where each one has his own album.
However, a question does arise here, what's the fate of my old pics on facebook ? How can I for example find all the tagged photos of some person ? That's a drawback.
The problem is much more general that it initially seems. The diversity of services is a good thing, both for competition and creativity and freedom of choice. However, some services are much much useful if aggregated among all your friends. Or at least if sharing of items is possible among different service providers, like calendar providers, image sharing, item recommendation.
Some solution has to be sought. And I conjecture that solving it is impossible because some unforeseen aggregation services might require user approval for privacy issues and then it can't be seamlessly done unless are friends in your network (and their network) are actively presented by the terms of the new value-added services of all different providers. That's impossible without centralized coordination and control over all humanity. It's just impossible.
So one solution to do so is to make the move you want in your local vicinity as much as you can. But it becomes tiring when lots of new services has shown and also when users tend to have keenness on their old service because of the effort need to be done to migrate all the data to the new service or at least the psychological effect of having to leave their old data (and sometimes for leaving the old familiar interface too).
So, by definition, multiple services existing together implies that users are distributed between them in some sort of a fair share. Adding support to unify and aggregate these services together requires at least some sort of unified identification per person. Which, although of existence of openID, is not always feasible for many people because they just don't like having single identifiable identity, or in other words "privacy".
Privacy became a concern in my eyes when I noticed that I almost can get enough information about a person through his public facebook data and his linked-in account to know his looks, and his friends/community and his educational/work background.
In the same sense having centralized identity with all the information can be a big privacy breach if the credentials is lost to some malicious individual/institution. Biometrics are not enough for it is not attainable by all people and even PKI infrastructure is not good enough for lack of central authority knowledge of identifying information of each individual on the face of earth, and for the (non-zero) possibility of private key loss !
Google tried to unify lots of services in its re-innovation of email, the so-called "google wave". It's still too early to judge it but I suppose that something too general can not be as good as something specific. For one simple reason, the additive complexity of adding more and more details to something over-generalized will eventually overhaul an individual because he might not be able to mentally organize all this information because to the mind it is still in one entity: google wave.
Even if google provides a universal communication service, it's still to be integrated into much more services. All blogs and all services with "commentable" contents has to support it to be really universal. However, even if that happened, the existence of provable trade-offs in human computer interaction for many factors including but not limited to: hardware costs, bandwidth limits, screen sizes, mobility, privacy, security, wide-spectrum usability, intuitive GUI, and nitty-gritty feature sets, makes it just infeasible to make one big universal communication service like google wave.
It might be solved with some sort of specialization, like google wave for the extreme-dull-mentallyRetarted-totallyUneducated-internetUnknowing-computerIlliterate-idiots, that is provided with totally different look and feel, and different set of simplified services. Then it can be feasible but the identification has to be different than "google wave", i.e. specialized, the opposite of general !
In conclusion, if you completed reading until this part then I know your name ;)
Picasaweb has several advantages over facebook from my point of view. The most important one is the ability to store images with original quality. Auto-tagging is also a great relief, that you can tag faces of people much much faster. Also, for shared events all people can upload to one common album, unlike facebook where each one has his own album.
However, a question does arise here, what's the fate of my old pics on facebook ? How can I for example find all the tagged photos of some person ? That's a drawback.
The problem is much more general that it initially seems. The diversity of services is a good thing, both for competition and creativity and freedom of choice. However, some services are much much useful if aggregated among all your friends. Or at least if sharing of items is possible among different service providers, like calendar providers, image sharing, item recommendation.
Some solution has to be sought. And I conjecture that solving it is impossible because some unforeseen aggregation services might require user approval for privacy issues and then it can't be seamlessly done unless are friends in your network (and their network) are actively presented by the terms of the new value-added services of all different providers. That's impossible without centralized coordination and control over all humanity. It's just impossible.
So one solution to do so is to make the move you want in your local vicinity as much as you can. But it becomes tiring when lots of new services has shown and also when users tend to have keenness on their old service because of the effort need to be done to migrate all the data to the new service or at least the psychological effect of having to leave their old data (and sometimes for leaving the old familiar interface too).
So, by definition, multiple services existing together implies that users are distributed between them in some sort of a fair share. Adding support to unify and aggregate these services together requires at least some sort of unified identification per person. Which, although of existence of openID, is not always feasible for many people because they just don't like having single identifiable identity, or in other words "privacy".
Privacy became a concern in my eyes when I noticed that I almost can get enough information about a person through his public facebook data and his linked-in account to know his looks, and his friends/community and his educational/work background.
In the same sense having centralized identity with all the information can be a big privacy breach if the credentials is lost to some malicious individual/institution. Biometrics are not enough for it is not attainable by all people and even PKI infrastructure is not good enough for lack of central authority knowledge of identifying information of each individual on the face of earth, and for the (non-zero) possibility of private key loss !
Google tried to unify lots of services in its re-innovation of email, the so-called "google wave". It's still too early to judge it but I suppose that something too general can not be as good as something specific. For one simple reason, the additive complexity of adding more and more details to something over-generalized will eventually overhaul an individual because he might not be able to mentally organize all this information because to the mind it is still in one entity: google wave.
Even if google provides a universal communication service, it's still to be integrated into much more services. All blogs and all services with "commentable" contents has to support it to be really universal. However, even if that happened, the existence of provable trade-offs in human computer interaction for many factors including but not limited to: hardware costs, bandwidth limits, screen sizes, mobility, privacy, security, wide-spectrum usability, intuitive GUI, and nitty-gritty feature sets, makes it just infeasible to make one big universal communication service like google wave.
It might be solved with some sort of specialization, like google wave for the extreme-dull-mentallyRetarted-totallyUneducated-internetUnknowing-computerIlliterate-idiots, that is provided with totally different look and feel, and different set of simplified services. Then it can be feasible but the identification has to be different than "google wave", i.e. specialized, the opposite of general !
In conclusion, if you completed reading until this part then I know your name ;)
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