What if the logic of our biology is non-Boolean?
Please bear with me as I explore this utterly speculative stream of thought.
As you know, among other things, I have been simultaneously working on two very different research topics:
Cancer Genomics and Measurement Based Quantum Computing.
As you may have read in my earlier posts on cancer genomics, we have a novel (tighter) formulation (that we solve via our Graver Augmented Multi-Seed Algorithm, GAMA) to discover mutated gene pathways. Additionally, we have argued that is also important to understand how the various gene pathways may be related to each other, and so proposed studying the Topology of Cancer Pathways.
The more I dug into cancer research, the more I have become suspicious that this binary logic of driver and passenger mutations, and dealing with sets of mutated genes – that is pathways – may not be the most fruitful way to frame cancer.
This particular article from Lancet Oncology triggered this stream of thought:
Yale Cancer Center Precision Medicine Tumor Board: two patients, one targeted therapy, different outcomes
It is a short article (2 pages) and I recommend you read in its entirety. Let me present their closing sentences here:
Although both patients’ tumours had a damaging ATM mutation, the difference in outcomes raises questions as to the variable effects of targeted therapies in patients with destructive mutations in the same gene.
Several reasons might underlie the disparate responses in these cases: different tumour types, different specific mutations in ATM, and differences in co-mutations and epigenetic regulation of gene expression.
Understanding the contribution of these and other factors to drug responses constitutes a major challenge to precision medicine as this field moves forward.
You may have also read my many posts on quantum computing.
The one that I want to mention here, Deep Beauty, discusses Category Theory and Topos, intuitionist (non-boolean) logic, and other such topics in pure mathematics.
In particular, Category Theory and Topos provide a credible alternative to the mainstream set-theoretic foundations of mathematics (that is inherently Boolean).
What if, instead of studying objects (such as mutated genes) and sets of those objects (pathways), using Boolean logic, we reframed
cancer as a process
and constructed an alternative mathematics for cancer genomics, using Category Theory and Topos, taking full advantage of the rich intrinsic contextuality that this majestic field of pure mathematics provides?
What if the logic of our biology is not as simple as that which can be represented by set-theoretic mathematical formalism and Boolean logic, and needs something vastly more capable to appropriately understand it?
What if our attempts to combat cancer have been handcuffed because we did not respect our biology sufficiently, and have been attempting to grasp its intricacies using mathematical methods (and so the computational algorithms) that are unsuited, infantile even, for this task and that we have not sufficiently respected Nature at the level of her sophistication?
I know it must be infuriating to cancer biologists when an outsider — from a Business School, for heaven’s sake — with scant knowledge, shoots from the hip.
You must want to toss my preposterous suggestion, in an apoplectic fit of anger (or amused disbelief at the silliness), into the dustbin of ridiculously ignorant proposals, and bury that in the graveyard of clueless ideas (that are DOA) generated by buffoons who fancy themselves as scientifically literate.
I get it. But, let me offer you this, a testament to my track record, when I have followed up on my instincts:
Observation 1. In the mid-to-late 1980s, in the field of Operations Research, there were many published papers that analyzed queuing systems using infinitesimal perturbation analysis (IPA). This research has had no noticeable impact on practice.
My Instinctive Insight 1. IPA should be applied to a different area, that of discrete time capacitated stochastic inventory models, and can form the computational backbone to tackle real world global supply chain inventory planning problems.
Outcome 1. This train of thought has led to the creation of Billions of dollars of shareholder value in Fortune 500/Global 2000 companies. (My enterprise software company SmartOps has been acquired by SAP.)
Observation 2. In the mid-to-late 1990s, in the field of Operations Management, there were many published papers that used Game Theory to analyze stylized discrete-time stochastic inventory models. This research has been inconsequential to the real-world practice of supply chain management.
My Instinctive Insight 2. Game Theory should be applied to queuing models in the context of healthcare operations.
Outcome 2. This train of thought led to modeling of the US Organ Transplant system as a network of overcrowded queues (with abandonment), and that multiple listing can be modeled as a selfish routing game on this network. Hundreds of additional transplants have taken place in the last few years . (See my social enterprise OrganJet for more details.)
This brings me back to cancer biology.
Observation 3. There are many published papers in Category Theory and Topos aimed at understanding quantum mechanics and foundations of physics. This research has yet to provide any new testable predictions.
My Instinctive Insight 3. Category Theory and Topos may be an appropriate framing to understand cancer biology.
Outcome 3. This train of thought led to…….
What if this is crazy enough to be useful?
You are welcome.