All the three above senses, their nature (quantitative), falls within the domain of physics and, by extension, mathematics — TheMadFool

That's an interesting observation. Which leads me to postulate that the Sixth Sense of Reason is also a sort of mathematical discrimination. Rational thought compares two or more ideas or objects in terms of ratios, evaluated on a range from 0 to100%, or False to True. I'm not sure what the cosmic implications of that might be, other than the Mathematical Universe hypothesis, or the Information Universe theory. Apparently everything in this world has a mathematical foundation, and Math is an abstract form of Generic Information. Perhaps the "number sense" is just a specialized aspect of the typical human ability to parse the world into qualitative Good / Bad relationships, relative to Me & Mine. :nerd:

:ok:

Update

I don't know if this is correct but last I checked odor and flavor (chemical) work like jigsaw puzzles - the agonist (scent/flavor) physically fits with the receptor (olfactory/gustatory). Geometry (shapes & space), a bona fide branch of mathematics.

Start with a bit more modernity than Aristotle's 5 senses.

https://www.press.jhu.edu/news/blog/how-many-senses-do-we-have

Reminds me of Pirsig's discussion of the motorbike part that does not appear in the parts catalogue because it's part of another part.

One discovers with age that proprioception in the manifestation of the ability to maintain balance, decays to the extent that one needs to integrate it with vision. Shut your eyes and you fall over. Is vision part of balance? Sometimes, definitely.

All the three above senses, their nature (quantitative), falls within the domain of physics and, by extension, mathematics — TheMadFool

All of the senses have a physical aspect but it's much too far a stretch to say that they therefore 'fall within the domain of physics'. Physics has many crises on its hand with the things it is meant to explain, namely, matter and energy, without even glancing at the various conundrums that are involved in accounting for the nature of sensory experience. Even given that sounds and colours have definite wavelengths and frequencies, electromagnetic or atmospheric, their assimilation into a cohesive meaningful cognitive act is not 'explained by physics'.

As for why it does not, and this might be a deraller, it's because the manner in which physical stimuli give rise to the subjective experience of colors, sounds, and moving objects, is precisely the subject of the well-known 'hard problem of consciousness' - so you'd better face up to it. And this has been validated by science so it's not just the abstract ramblings of an Arts faculty member.

I've long been interested in that Eugene Wigner paper, in fact it was one of the first things I ecountered on the philosophy forum that preceded this one. But it doesn't have much bearing on what you have written. The meaning of Wigner's paper is not regarding whether the universe or things in it can be represented mathematically, but why it is that mathematical reasoning is so uncannily predictive and explanatory in the natural sciences. In other words, the amazing thing about mathematical reasoning is the mathematical faculty itself, and what it says about the nature of reason and the universe. (Einstein said 'the most incomprehensible thing about the world is that it is comprehensible'.)

Wigner's paper touches on that, but offers no explanation for it (it contains 12 instances of the word 'miracle'.) But to get into that subject in any depth is the philosophy of mathematics, which is almost innaccessible to the layman.

I've long been interested in mathematical realism or Platonism, the argument that numbers are real independently of any individual mind. It is not a popular view in academia, because if numbers are real, but not material, then that falsifies materialism, which breaks an implicit taboo in contemporary discourse. I've just found a very good textbook on it, although it's very expensive and I may not be able to understand much of it, not being well educated in mathematics.

Apparently everything in this world has a mathematical foundation, and Math is an abstract form of Generic Information. — Gnomon

Is it that the world has a mathematical foundation or that the ability to measure and count is what enables us to get its measure? Math starts with the process of abstraction, whereby the measurable attributes of a given phenomenon are abstracted and quantified. But it's not as if that mathematical abstraction is inherent in the object, rather it is the only means by which we can subjugate the object to mathematical analysis. 'Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover', said Russell. But the fascinating thing which Wigner comments on, is that aspects of reality are predicted by mathematics, which then turn out to be empirically true. (Not always - there are also arguments that physics has become lost in math.) That's the sense in which the world seems to be mathematical, but I think it's a mistake to believe that its mathematical nature is objective; I suspect that the mathematical nature of the world rather indicates the power of reason to grasp the deeper nature of reality. But that sits uncomfortably with naturalism.

@TheMadFool - I've had a go at you in the past for dropping pointless youtubes into threads but this particular one, Roger Penrose on whether maths is invented or discovered, is directly on target.

This excellent read might be helpful:

The Number Sense, Stanislas Dehaene — 180 Proof

Interesting video. I'm not a fan of Penrose (Nobel & work with Stephen Hawking et al notwithstanding). My two bits – pure mathematics is discovered, applied mathematics is invented. A spinozist (à la Tegmark) rather than platonist (à la Gödel) bias.

Start with a bit more modernity than Aristotle's 5 senses.

https://www.press.jhu.edu/news/blog/how-many-senses-do-we-have — unenlightened

An eye-opener, thanks! It doesn't seem to vitiate my point though which is we can mathematize sense perception. Right?

the Sixth Sense of Reason is also a sort of mathematical discrimination. — Gnomon

To the extent that math is defined as the analysis of patterns, yes. Argument forms (modus ponens, modus tollens, disjunctive syllogism, etc. in logic) are patterns in reasoning.

The senses of taste and smell which I, thanks to you, realized are geometric i.e. mathematical in nature (the receptor-agnoist theory claiming that the agonist fits like a jigsaw piece with the receptor, the matching other piece).

Can we somehow translate thoughts (logic and others) into geometry and arithmetic like we can with the senses (see OP)? The bottom line is that from a physicalist point of view, thoughts are bioelectricity, amenable to mathematization (physics) which raises interesting questions about physicalism.

All of the senses have a physical aspect but it's much too far a stretch to say that they therefore 'fall within the domain of physics'. Physics has many crises on its hand with the things it is meant to explain, namely, matter and energy, without even glancing at the various conundrums that are involved in accounting for the nature of sensory experience. Even given that sounds and colours have definite wavelengths and frequencies, electromagnetic or atmospheric, their assimilation into a cohesive meaningful cognitive act is not 'explained by physics'. — Wayfarer

Methinks a nonphysicalist has nothing to worry about when it comes to physics as, from what I've read and heard, physics is well on its way to becoming a branch of mathematics - mathematical models being some kinda primary resource for physical hypotheses/theories (the theory of relativity, for instance, is 4 dimensional geomtery). In other words, when we're discussing physics what we're actually dealing with is math (numbers, shapes, etc.) and therein lies the rub - are numbers (immaterisl abstractions) real?

I've long been interested in that Eugene Wigner paper, in fact it was one of the first things I ecountered on the philosophy forum that preceded this one. But it doesn't have much bearing on what you have written. The meaning of Wigner's paper is not regarding whether the universe or things in it can be represented mathematically, but why it is that mathematical reasoning is so uncannily predictive and explanatory in the natural sciences. In other words, the amazing thing about mathematical reasoning is the mathematical faculty itself, and what it says about the nature of reason and the universe. (Einstein said 'the most incomprehensible thing about the world is that it is comprehensible'.) — Wayfarer

I included Wigner's paper for discussion because the fact that "...mathematical reasoning is so uncannily predictive and explanatory in natural sciences" might be the smoking gun that the universe itself is fundamentally, at its core, mathematical and that begs the question, "is all that's real just numbers?" Numbers, we're certain, are immaterial abstractions. What does that lead to?

I've had a go at you in the past for dropping pointless youtubes into threads but this particular one, Roger Penrose on whether maths is invented or discovered, is directly on target. — Wayfarer

:grin: I watched that video (again). Interesting to say the least. His opinion, from what I gathered, is that math is both invented and discovered.

This excellent read might be helpful:
The Number Sense, Stanislas Dehaene
— 180 Proof — 180 Proof

:ok: Thanks.

My two bits – pure mathematics is discovered, applied mathematics is invented. A spinozist (à la Tegmark) rather than platonist (à la Gödel) bias. — 180 Proof

A transcript of an interview by Hannah Fry (mathematician):

Hannah Fry: Is math invented or discovered?

Hiranya Peiris (Professor of Astrophysics, University College London): Invented!

Dr. Eleanor Knox (Philosopher of Physics, King's College London): Discovered!

Sylvester James Gates (Professor of Physics & Mathematics, Brown University): Both!

Brian Greene (Professor of Physics & Mathematics, Columbia University): I have no idea!

Penrose the only one of his ilk that makes a lick of sense to me.

[Penrose's] opinion, from what I gathered, is that math is both invented and discovered. — TheMadFool

But the fact that it is in part discovered, and not wholly invented, tends to favour mathematical realism.

Numbers, we're certain, are immaterial abstractions. What does that lead to? — TheMadFool

The stream of human knowledge is heading towards a non-mechanical reality. The universe begins to look more like a great thought than a great machine. Mind no longer appears to be an accidental intruder into the realm of matter. We are beginning to suspect that we ought rather to hail it as the creator and governor of this realm. — Sir James Jeans

:lol: Well then, I'm in good company!

↪180 Proof Penrose the only one of his ilk that makes a lick of sense to me. — Wayfarer

Why ain't I surprised? ([cough]microtubules[/cough]) :zip:

@Wayfarer

The universe begins to look more like a great thought than a great machine — Sir James Jeans

:fire:

But the fact that it is in part discovered, and not wholly invented, tends to favour mathematical realism. — Wayfarer

Yep! I don't think The Unreasonable Effectiveness Of Math In The Natural Sciences is just a coincidence. Coincidences are one-off events and don't display such consistency.

One reason I wished to discuss the senses, specifically taste and smell, was they appeared to be qualitative (nonmathematical) instead of quantitative (mathematical) and that made me question Max Tegmark's Mathematical Universe Hypothesis and Eugene Wigner's The Unreasonable Effectiveness of Mathematics In The Natural Sciences.

However, it turns out I was wrong, smell and taste can be rendered as a geometric interaction between differently shaped molecules, these shapes themselves reducible in soms sense to arithmetic (charge, force, etc.).

To All Interested

It looks like red is the number 650 nm (wavelength).

Redness, is in philosophy of mind, a subjective experience and yet, as we see here, redness is an objective truth in that it's light with a wavelength 650 nm.

Mary's Room (Knowledge argument) [Physicalism/Nonphysicalism]

Well then, I'm in good company! — 180 Proof

Indeed! :grin:

smell and taste can be rendered as a geometric interaction between differently shaped molecules — TheMadFool

This doesn't do justice to the difference between sensory and rational faculties. Being able to count and see rational relations is different in kind from sensory perception.

@Wayfarer

By the way, Roger Penrose has made a name for himself in tesselation mathematics (tiling) and receptor-agonist theory of how smell and taste work, to my reckoning, is a step in the direction of 3D tesselations/tilings. A meaningful coincidence (Jung's synchronicity).

smell and taste can be rendered as a geometric interaction between differently shaped molecules
— TheMadFool

This doesn't do justice to the difference between sensory and rational faculties. Being able to count and see rational relations is different in kind from sensory perception. — Wayfarer

Mathematics Anxiety (Mathemaphobia)

Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p. 1). The academic study of math anxiety originates as early as the 1950s, where Mary Fides Gough introduced the term mathemaphobia to describe the phobia-like feelings of many towards mathematics. — Wikipedia

Watch the video below, a conversation between astrophysicist Neil deGrasse Tyson and evolutionary biologist Richard Dawkins on why most people are bad at math?



Notice how logic and math are like Siamese twins - we can't seem to be able to talk about one without talking about the other.

If we're bad at math & logic, what does that mean for the belief that our universe is mathematical? It's like a person who's hard of hearing feeling ecstatic about music. What's the use? Fae can't hear it.

Being able to count and see rational relations is different in kind from sensory perception.

Being able to count and see rational relations is different in kind from sensory perception. — Wayfarer

How? Why? Please explain. Thanks

When you ask for an explanation, or a reason, you’re not asking for a visual impression. If you asked me, I don’t know, to show you a design or a picture, you’re asking for something visual. When you say ‘why is this different from that’ then you’re appealing to a faculty which is completely different from the visual faculty or from any sensory faculty.

It interests me that this is something that has to be explained, I would have thought it self-evident.

When you ask for an explanation, or a reason, you’re not asking for a visual impression. If you asked me, I don’t know, to show you a design or a picture, you’re asking for something visual. When you say ‘why is this different from that’ then you’re appealing to a faculty which is completely different from the visual faculty or from any sensory faculty.

It interests me that this is something that has to be explained, I would have thought it self-evident. — Wayfarer

Well, I attempted, as best as any math-illiterate person can, to mathematize an argument form like, say, modus ponens, but no success there and it seems to do this to hold the wrong end of the stick, have it backwards so to speak :point: Logicism.

The only numbers I see in modus ponens are the ordinal numbers used as references for the premises and the conclusion:

1. $P \rightarrow Q$

2. $P$

Ergo,

3. $Q$

In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano. — Wikipedia

We must also not forget that all thoughts are, as per existing scientific paradigms, bioelectricity and electricity is physics and physics is math. Paradoxically, the hardcore nonphysicalist should be happy about physicalist reduction of psychological states to brain states (bioelectricity) because then, fae only needs to continue along that same trajectory and reduce brain states to mathematics. As you can see, we've managed to, with only a little effort, remove physicalism from the equation.

I dunno!

My English must be dreadful.

My English must be dreadful. — Wayfarer

Perhaps you're unable to put into words your intuitions on the matter. Happens all the time to even the best among us. Do try to come up with a coherent statement. Until then...sayonara.

Wouldn’t make any difference, I fear.

Wouldn’t make any difference, I fear. — Wayfarer

:ok:

One reason I wished to discuss the senses, specifically taste and smell, was they appeared to be qualitative (nonmathematical) instead of quantitative (mathematical) — TheMadFool

Qualitative does not imply nonmathematical. For example, it used to be said that topology is math without numbers, although that's not entirely true.

Qualitative does not imply nonmathematical. For example, it used to be said that topology is math without numbers, although that's not entirely true. — jgill

Yes, that's the other issue I wanted to discuss. For example the type specimen of quality has been, if I'm not mistaken, color i.e. people are under the impression that color is a quality but as pointed out in the OP, redness is the quantity 650 nm. So, the question, are qualities, therefore, actually quantities?

Also note, when Max Tegmark's Mathematical Theory Of The Universe and Eugene Wigner's The Unreasonable Effectiveness Of Math In The Natural Sciences refer to the quantitative nature of reality.

Last but not the least, kindly, if you don't mind that is, summarize topology in around 2 - 3 paragraphs for me. I'd like to know how math is, in addition to being quantitative, also qualitative. Much obliged. Thanks.

I know it's trite, but imagine a maleable plastic doughnut being continuously deformed into a coffee cup. The notion of continuous transformations from one object to another is the fundamental topological characteristic. The more technical aspects involve open sets. If X is a non-empty set, a class T of subsets of X is called a topology on X provided (1) unions of sets in T are sets in T, and (2) intersections of finite collections of sets in T are sets in T.

The study of topology begins with point-set topologies - and I have fond memories of being introduced to these in 1962 and teaching them during the last quarter of the past century - and proceeds to esoteric terrains I dare not tread.

As G. F Simmons said, "A topological space can be thought of as a set from which has been swept away all structure irrelevant to the continuity of functions defined on it".

I know it's trite, but imagine a maleable plastic doughnut being continuously deformed into a coffee cup. The notion of continuous transformations from one object to another is the fundamental topological characteristic. The more technical aspects involve open sets. If X is a non-empty set, a class T of subsets of X is called a topology on X provided (1) unions of sets in T are sets in T, and (2) intersections of finite collections of sets in T are sets in T.

The study of topology begins with point-set topologies - and I have fond memories of being introduced to these in 1962 and teaching them during the last quarter of the past century - and proceeds to esoteric terrains I dare not tread.

As G. F Simmons said, "A topological space can be thought of as a set from which has been swept away all structure irrelevant to the continuity of functions defined on it". — jgill

So, the idea behind topology is to discover whether one object with given geometric properties can be transformed into another object i.e. it's kinda like the ancient magical art of shapeshifting (werewolves):

Start with a bit more modernity than Aristotle's 5 senses.

https://www.press.jhu.edu/news/blog/how-many-senses-do-we-have — unenlightened

Why not start with everything, and eliminate by a process of elimination all that is not sense, and proceed from there.

Why not start with everything, — god must be atheist

It's unavailable.

Apparently everything in this world has a mathematical foundation, and Math is an abstract form of Generic Information. — Gnomon
Is it that the world has a mathematical foundation or that the ability to measure and count is what enables us to get its measure? Math starts with the process of abstraction, whereby the measurable attributes of a given phenomenon are abstracted and quantified. But it's not as if that mathematical abstraction is inherent in the object, rather it is the only means by which we can subjugate the object to mathematical analysis — Wayfarer

I agree. When I said that the physical world has a mathematical foundation, I was referring to the pattern of inter-relationships that the human mind interprets as Logic. Math is not a physical object, but a metaphysical network of relative values (relationships ; proportions). The interpreted values, or meaningful patterns, are not inherent in any particular thing, but are evaluated by the observing mind, relative to self and to the whole system. Einstein's Special Relativity applies to physical objects. But General Relativity includes the subjective observer in the network, as a node in the whole pattern, by taking a god-like perspective, from outside the system looking in.

As I view it, the rational Mind "measures" those invisible links between things, and assigns both numerical values and emotional values. The numerical values are abstractions that we can convey to others in language, including mathematical notation. But the emotional values must be inferred from the behavior of the observer, including inflections of speech and emoticons in text. Disclaimer : I don't really know what I'm talking about. I'm just extrapolating from my personal worldview of Enformationism. :wink:


Logos :
Greek term meaning “word”, “reason”, “proportion”. It was used by philosophers in a technical sense to mean a cosmic principle of order and knowledge. In ancient Greek philosophy and theology, Logos was the divine Reason implicit in the cosmos, ordering it and giving it form and meaning.
http://blog-glossary.enformationism.info/page14.html
Note -- Reason is applied Logic, which "enables us" to recognize the design (order, organization ; form) in the objects of our perception. The mental evaluation of such an observation is what we call a Concept.

PATTERN RECOGNITION :

:ok:

Einstein's Special Relativity applies to physical objects. But General Relativity includes the subjective observer in the network, as a node in the whole pattern, by taking a god-like perspective, from outside the system looking in — Gnomon

I think both special and general include observers. That's not the usual distinction. Accelerated motion and other features are considered in general.

Einstein's Special Relativity applies to physical objects. But General Relativity includes the subjective observer in the network, as a node in the whole pattern, by taking a god-like perspective, from outside the system looking in — Gnomon
I think both special and general include observers. That's not the usual distinction. Accelerated motion and other features are considered in general. — jgill

I doubt that Einstein himself made the distinction I was referring to. It was just my interpretation. I was extrapolating from the terms "Special Relativity" (reductive) and "General Relativity" (holistic). If my reference to "Einstein" -- to make a long story short -- seems wrong to you, please delete the name from the sentence. It's not essential to the concept. :smile: