There is much more about these chemical transactions and their proofs. First is that transactions are partially independent on the molecules. The blockchain may be useful only for having a distributed database of transactions and proofs, available for further use. But there’s more.
Think about this database as one of valid computations, which can then be reused in any combination or degree of parallelism. Then, that’s the field of several competitions.
The same transaction can have several proofs, shorter or longer. It can have big left pattern therefore costly to use it in another computation. Maybe a transaction goes too long and therefore it is not useful to use in combination with others.
When there is a molecule to reduce, the application of a transaction means:
– identify a subgraph isomorphic with the left pattern and pick one such subgraph
– apply the transaction to this particular subgraph (which is equivalent with: reduce only that subgraph of the molecule, and freeze the rest of the molecule, but do it in one step because the sequence of reductions is already pre-computed)
Now, which is more convenient, to reduce the molecule by using the random algorithm and the available graph rewrites, or to use some transactions which fit, which is fast (as concerns step 2) but costly (as concerns step 1), moreover it may be that there is a transaction with shorter proof for that particular molecule, which mixes parts of several available precomputed transactions.
Therefore the addition of transactions and their proofs (needed to be able to validate them) into the database should be made in such a way which profit from this competition.
If I see the reduction of a molecule (which may be itself distributed) as a service then besides the competition for making available the most useful transactions with the shortest proofs, there is another competition between brute force reducing it and using the available transactions, with all the time costs they need.
If well designed, these competitions should lead to the emergence of clusters of useful transactions (call such a cluster a “chemlisp”) and also to the emergence of better strategies for reducing molecules.
This will lead to more and more complex computations which are feasible with this system and probably fast enough they will become very hard to understand by a human mind, or even by using IT tools on a limited part of the users of the system.
By definition a transaction is either a rewrite from the list of
accepted rewrites (say of chemlambda) or a composition of two
transaction which match. A transaction has a left and a right pattern
and a proof (which is the transaction expressed as a cascade of
When you reduce a molecule, the output is a proof of a transaction.
The transaction proof itself is more important than the molecule from
the start. Indeed, if you think that the transaction proof looks like
where leftpattern1 is a list of lines of a mol file, same for the rightpattern1,
then you can deduce from the transaction proof only the following:
– the minimal initial molecule needed to apply this transaction, call
it the left pattern of the transaction
– the minimal final molecule appearing after the transaction, call it
the right pattern of the transaction
and therefore any transaction has:
– a left pattern
– a right pattern
– a proof made of a chain of other transaction which match (the right
pattern of transaction N contains the left pattern of transaction N+1)
It would be useful to think in term of transactions and their proofs
as the basic objects, not molecules.
I’m thinking about money lately and I want to share with you a definition of money related to cloning. It may be relevant to virtual currencies.
What is money in an exchange transaction? In such a transaction there are two parts, say Alice and Bob. There are two items involved in the transaction, call them A and B.
Before the transaction:
- Alice has A
- Bob has B
After the transaction:
- Alice has B
- Bob has A
The question is: which one, A or B, is money? Mind that there are exchanges where none of them is money.
The proposed answer is the following: the money is that item which is hard to clone for both Alice and Bob and the transaction is made for the other item, which is hard to clone for only one part, Alice or Bob.
More clearly, say Alice has the money, item A. She cannot clone it, nor can Bob. So she exchanges it for B (say a pair of shoes), which is hard for Alice to clone (that’s why she obtains it from an exchange), but is easier for Bob to clone (that’s why he sells it, getting in exchange a hard to clone item).
So if we have a system where p2p exchanges are possible, then the money will be those items which are exchanged because they are hard to clone by everybody, and they will tend to be exchanged for items which are easy to clone by at least somebody.
If any of the hard/easy cloning properties change, then money disappear:
- mints are cloning devices for real money, but if it becomes easy to mint money otherwise then that’s no longer money
- for real or virtual money, of one can double spend a money item, it means it can be cloned, so it ceases to be money
- money has to be scarce, as an effect of the fact it can’t be cloned
- if a coin made of gold, minted by a king, is in circulation, then at some point the technology allows to clone it, for example by taking from each coin a minute amount of gold and mint new coins from this extra gold, by using a forged mint (for a virtual equivalent see the Ethereum gas-related hacks)
- money has to be hard to clone “objectively”, i.e. it is not enough to declare that money is hard to clone. There has to be some provably hard way to clone it.
This is a note about a simple use of convex analysis in relation with neural networks. There are many points of contact between convex analysis and neural networks, but I have not been able to locate this one, thanks for pointing me to a source, if any.
Let’s start with a directed graph with set of nodes (these are the neurons) and a set of directed bonds . Each bond has a source and a target, which are neurons, therefore there are source and target functions
so that for any bond the neuron is the source of the bond and the neuron is the target of the bond.
For any neuron :
- let be the set of bonds with target ,
- let be the set of bonds with source .
A state of the network is a function where is the dual of a real vector space . I’ll explain why in a moment, but it’s nothing strange: I’ll suppose that and are dual topological vector spaces, with duality product denoted by such that any linear and continuous function from to the reals is expressed by an element of and, similarly, any linear and continuous function from to the reals is expressed by an element of .
If you think that’s too much, just imagine to be finite euclidean vector space with the euclidean scalar product denoted with the notation.
A weight of the network is a function , you’ll see why in a moment.
Usually the state of the network is described by a function which associates to any bond a real value . A weight is a function which is defined on bonds and with values in the reals. This corresponds to the choice and . A linear function from to is just a real number .
The activation function of a neuron gives a relation between the values of the state on the input bonds and the values of the state of the output bonds: any value of an output bond is a function of the weighted sum of the values of the input bonds. Usually (but not exclusively) this is an increasing continuous function.
The integral of an increasing continuous function is a convex function. I’ll call this integral the activation potential (suppose it does not depends on the neuron, for simplicity). The relation between the input and output values is the following:
for any neuron and for any bond we have
This relation generalizes to:
for any neuron and for any bond we have
where is the subgradient of a convex and lower semicontinuous activation potential
Written like this, we are done with any smoothness assumptions, which is one of the strong features of convex analysis.
This subgradient relation also explains the maybe strange definition of states and weights with the vector spaces and .
This subgradient relation can be expressed as the minimum of a cost function. Indeed, to any convex function is associated a sync (means “syncronized convex function, notion introduced in )
where is the Fenchel dual of the function , defined by
This sync has the following properties:
- it is convex in each argument
- for any
- if and only if .
With the sync we can produce a cost associated to the neuron: for any , the contribution to the cost of the state and of the weight is
The total cost function is
and it has the following properties:
- for any state and any weight
- if and only if for any neuron and for any bond we have
so that’s a good cost function.
- take to be the softplus function
- then the activation function (i.e. the subgradient) is the logistic function
- and the Fenchel dual of the softplus function is the (negative of the) binary entropy (extended by for or and equal to outside the closed interval ).
 Blurred maximal cyclically monotone sets and bipotentials, with Géry de Saxcé and Claude Vallée, Analysis and Applications 8 (2010), no. 4, 1-14, arXiv:0905.0068
The “State of surveillance”with Edward Snowden and Shane Smith concentrates on state surveillance. This is a complex problem, but the gist of it is that they collect metadata. My first, gut reaction, was: the whole IT industry is now based on collecting metadata.
Not only states do it, but every big IT company is based on metadata. They could not work without collecting metadata.
The scary potential of metadata use by states does not change the fact that the economic models behind today big IT companies are built around metadata. So, no matter how concerned we may be about the states, no matter how hard people push for laws which would limit the state’s metadata collection, all this has no serious effect.
I don’t think that coercion, by law or otherwise, is the effective thing to do. It’s hypocritical and makes people feel good about themselves, but, really, how can it work? Are those people going to stop using every free (aka your metadata are the product) service too? No way, it’s not going to happen.
Let’s ask: why do we need metadata? Can’t we make systems which do not need metadata to function?
I think that we can’t, as long as we stay in the IT paradigm. Metadata is data about data, a special kind of data which has to be shared between the sender and the receiver of information.
In the biology world, metadata functions differently. That tree from the jungle selects the pollinator bird by the shape of it’s flower. However, the bird does not need to know the identity of the tree, nor the tree ever needs to know exactly which bird, among those with the beak of the right size, is going to pollinate it. “Knowing” does not even make sense, for them.
The humble fly does not need to know euclidean geometry in order for it’s brain to “process data” harvested by the visual system in order to activate the muscles. It doesn’t even make sense, in principle, to think like that. The scientist presents the evidence for that in such terms.
I don’t need to know the name and address of the guy I randomly meet on the street and ask him for directions, although, of course, if a third party films us then there is evidence showing that I and the guy with that identity (recoverable from other evidence) have met, because we are at about the same space coordinates, at about the same time coordinate, and we signaled with our bodies the willingness to exchange information, according to the video and ambiental sound evidence.
The biggest weakness of the IT paradigm is metadata. Prove me wrong.
Congratulations! Via a comment by roy. If there is any other news you have then you’re welcome here, as in the old days.
Bruce Dell has a way to speak, to choose colors and music which is his own. Nevertheless, to share the key speaker honor with Steve Wozniak is just great.
It rubs me a bit in the wrong direction when he says that he has the “world first new virtual lifeforms” at 7:30. Can they replicate? Do they have a metabolism? On their own, in random conditions?
If I sneeze in a Holoverse room, will they cough the next day? If they run into me, shall I dream
new ideas about bruises later?