The change in outlook which led to modern physics and its mathematics thus might, extended to biology, lead to a new, more flexible, more temporalist paradigm (and perhaps to a new
mathematical understanding of biology).
«A breakthrough on
the mathematical understanding of Einstein's equations.»
Godsoe used probability theory to formally connect observations of where species actually occur to
mathematical understanding of species ecology.
Most importantly, they are prepared to take best advantage of educational technologies for fostering
the mathematical understanding of their students both now and in the future.
It is a distinctive feature of the modern
mathematical understanding of the Navier - Stokes equations that not all problems are going to be solvable with any accuracy at all.
But most real estate investors have
a mathematical understanding of what cashflow is but not a conceptual one.
Not exact matches
The other key
mathematical driver to
understanding our business model is that we invest in < 1 %
of the deals that we see every year.
Beyond thinking a million - pound payout is a matter
of basic necessity, he is deeply insecure in his professional standing, confessing he no longer
understands the «immensely complicated
mathematical formulae» that drive his industry.
Though savvy investors, like Shakespeare's Antonio, have long
understood the benefits
of diversification, it was not until the 1950s when an academic named Harry Markowitz introduced research on what he called modern portfolio theory that people were able to
understand diversification in an objective,
mathematical sense.
Do you know the
mathematical impossibility that even one
of these could randomly come into existance?Let alone all
of the building blocks required for just a single simple cell to come together to form any type
of living thing?There sure should be some blobs
of fossilized transitions if evolution could happen.You people are real smart why don't you quit bashing Christians and quit believing the garbage you have been fed, and look up the evidence put forth by the Creation Research people.They have in fact proven creation down to a cellular level.Unlike evolution scientists who have no answers, but cleverly devised fables.Evolution is not even a very good fairy tale.Even if I didn't believe in God, Evolution is such a fools explanation
of the origin
of man that it takes just that to even consider it true.I
understand though that you athiests will believe anything that allows you to love your sin and hatred
of the one true God.
What I really don't
understand is how you ignore all the other sign in the bible that are to tell
of the end
of days and believe a man that has come up with a
mathematical equation!
Superstring theory has a
mathematical structure so sophisticated that, after a quarter
of a century
of study by hundreds
of the world's most brilliant physicists and mathematicians, it is still not fully
understood.
But we may, I think, conclude with Errol Harris (AT 74) that from the Hegelian perspective, the philosophical shortcomings
of classical logic extend to
mathematical logic as well, and that as logic
of the
understanding, both deal with the «abstract concept
of class or aggregate,» and are both inextricably connected with a metaphysics
of externally related particulars that lose themselves in a «spurious infinite,» and with a concomitant mechanical cosmology.
This means that Cantor's «
mathematical paradise» should be
understood as follows: Let there be a
mathematical universe such that sets constitutive
of it have the defining feature that a part
of the set is equal to the whole
of the set.
But if we
understand Whitehead in light
of the
mathematical model, then his identification
of the extensive continuum with the most general limitation upon general potentiality, the fundamental determination
of order in this epoch (PR 103, 148), does not represent confusion but straightforward metaphysics.
But we
understand and judge Whitehead to be a realist, and so he must have an analysis
of creative advance which gets around the problems that arise when time and space are allowed to be isomorphic with the
mathematical continuum, the problem with which is that its series are dense rather than discrete.
Mathematics is the most powerful technique for the
understanding of pattern and for the analysis
of the interrelationship
of patterns... In the next 2,000 years the overwhelming novelty in human thought will be the dominance
of mathematical understanding... Applied mathematics is the transference
of this study to other examples
of the realization
of these patterns.
In my scientific suppositions I have proposed that their were once immeasurably unknown amounts
of Big Bangs spread out uniformly upon the great vastness
of spatial relativisms that is Nothingness itself... Such a theory regarding unknowable amounts
of Big Bangs spread out uniformly upon the great vastness
of continual Nothingness just may well be the missing
mathematical linkage for explaining the hindering smallness
of celestial issues that has confounded many astrophysicists who endeavor to seek a
mathematical formulary in order to rationalize a theoretical
understanding of the celestial cosmos...
Alongside and dependent on the rich development
of aesthetic, scientific, and
mathematical distancing arose other modes
of understanding man, which were called forth initially by the practical exigencies
of political life.
«39 Since few people read Lowe's entire 1949 article in which the details
of his argument are really presented, I will select a few
of the key contrasts Lowe reprinted in
Understanding Whitehead, which contains an abridgement of the 1949 article, in an effort to show that Gunter has really answered them already rendering Whitehead not so much Bergson's mathematical alter ego, 40 as something more approaching his philosophical blood brother 41 According to Lowe, however, «it is fatal to the understanding of Whitehead's constructive metaphysical effort to define it in Berg
Understanding Whitehead, which contains an abridgement
of the 1949 article, in an effort to show that Gunter has really answered them already rendering Whitehead not so much Bergson's
mathematical alter ego, 40 as something more approaching his philosophical blood brother 41 According to Lowe, however, «it is fatal to the
understanding of Whitehead's constructive metaphysical effort to define it in Berg
understanding of Whitehead's constructive metaphysical effort to define it in Bergsonian terms.
One might as well try to say ducks know nothing
of water as impugn Bergson's
mathematical understanding.
Neither man, however, had what Plato, also enthusiastic about mathematics, did have, a sagacious
understanding of the difference between
mathematical concepts and concrete actualities.
In his 1959 essay entitled «My Present View
of the World,» he argued that the fundamental entities are discrete but overlapping «events,» that the fundamental entities
of mathematical physics are «constructions composed
of events,» and that entities like conscious minds and «selves» are best
understood as collections
of events «connected with each other by memory - chains backward and forwards.
As Craig Dykstra has observed, Farley tends to limit the scope
of his
understanding of «cognition» to linguistic and logical —
mathematical realms.
Nature is in fact always much richer and more complex than our imaginative and
mathematical models, and we unduly shrivel our
understanding of the cosmos if we equate it in a simple way with our scientific schemes.
In his exposition
of Psalm 90 he even used the daring metaphor that the subject
of faith was a
mathematical point, so far was he from regarding faith as a subjective experience through which man's
understanding of himself is illuminated, and so exclusively should faith be defined in reference to its object, the extra se
of the historic Christ.
In that revolutionary address he unified geometry and physics into a single set
of axioms by symbolic logic.2 While the memoir does not comment theologically, it does propose a theory
of intersection points, or interpoints, which in its
mathematical abstraction suggests a lucid and stimulating model for projecting Whitehead's
understanding of God's relation to space.
I
understand that given the
mathematical impossibility
of hundreds
of thousands
of working parts randomly / accidently being formed into the first, simple reproducing life form, intelligent design not only makes a lot
of sense it's an absolute requirement.
Science as it is usually
understood is simply incapable
of addressing the question
of the possible purpose
of nature since the material it deals with has already been abstracted out
of the «qualitative» realm
of value and placed in that
of the merely quantifiable, subject only to
mathematical calculation.
The modern secular man, who probably can not
understand mathematical physics but has heard
of the Principle
of Relativity and the Quantum Theory, does not realize how much this kind
of thinking penetrates his thought processes.
Their resistance may be motivated by a fear that nature will slip out
of the control
of our mechanical and
mathematical models for
understanding physical reality, or it may be occasioned simply by our innate passion for order and intelligibility.
Another way
of understanding «chance» is the
mathematical.
The «Scientific Revolution» is so named because the success
of its
mathematical, experimental and developmental methodology realigned not just Aristotelian cosmology but also his
understanding of the «nature»
of things.
Acknowledgment
of the existence
of this rational dimension
of reality is vital to the possibility
of understanding the origin
of human
mathematical powers.
These «two poles» involve respectively the «presupposition
of] the
mathematical structure
of matter, its intrinsic rationality, which makes it possible to
understand how matter works and use it efficiently», which wonderfully «correspond ^ with] our spirit», and our own experimental activation
of «nature's capacity to be exploited for our purposes».
In this Biffi depicted Anselm's perspective as, contrary to much modern emphasis, grasping that «reality as a whole is much greater than we grasp through simple natural
understanding, substantiated solely by sensory experience, inductive and deductive reasoning,
mathematical calculation -LSB-...] faith not only is not separable from reason, and does not harm it, but is even the greatest and highest exercise
of our intellectual faculty.»
■ Bishop Nicholas
of Oresme (1323 - 1382), Bishop
of Lisieux who as a mathematician discovered how to combine exponents and developed graphs
of mathematical functions and as a physicist explained the motion
of the Sun by the rotation
of the Earth and developed a more rigorous
understanding of acceleration and inertia.
We are therefore able to
understand that some
of the physical quantities are born out
of the more qualitative
mathematical structures
of sense experience as a straightforward quantification thereof.
There can never be an absolutely final translation
of the New Testament, for (1) we do not know with
mathematical precision what its authors meant or how their readers
understood them, and (2) our own language changes from age to age and words acquire and lose meanings.
This is too complex an issue to discuss here, but I would submit that if
understanding rather than prediction is the goal
of science, models can not be replaced by predictive
mathematical formalisms.
Far more important is to give your children an
understanding of mathematical concepts which will enable them to use their calculators intelligently.
The latter can be found in more successful teaching programs — like the one at Waldorf School
of Baltimore — that are based on inquiry - based learning, and on students» self - evaluation
of their
understanding of mathematical formulas and theories.
A number
of recent news stories have had a similar kind
of message: animals viscerally
understand certain
mathematical operations better than humans do.
Shostak also brought up a less frightening but perhaps more existentially dreadful possibility about some future first contact: what if we finally hear from aliens broadcasting their presence as sentient beings, and the big announcement is their
understanding of well - known
mathematical phenomena such as the Fibonacci sequence.
As one can classify the shapes
of objects based on the
mathematical concept called topology, an exotic phase
of quantum matter can be
understood with underlying topology and symmetry in physical materials.
Applying new math, Kristina Crona, an American University assistant professor who researches in the area
of mathematical biology, and her colleagues show how ranking pathogen mutants can help scientists
understand how mutants evolve to resist drug treatments.
The author offers a comprehensive account
of his perspective on our
understanding of the physical behavior
of the universe and the
mathematical theory that underlies it.
Your online traces are helping fuel a revolution in the
understanding of human behaviour — one that's revealing the
mathematical laws
of our lives
Lipton and others are still trying to
understand the details
of Deolalikar's proof, but it essentially works by applying a type
of P equation to an NP problem, then showing that it won't work for deeply
mathematical reasons.
The solution to the Kirchhoff - Plateau problem not only contributes to the
understanding of energy minimizing
mathematical shapes, but can also be applied to biological systems.