I think it's fundamentally a question of incentives. A mathematician's career prospects and status depends heavily on being able to prove things that others can't. Why spend extra time helping your 'competitors'? Not saying this is ideal, but it seems to explain many behaviours in the community, and it seems unavoidable given the ever-increasing competition for jobs.
The Fourier transform of the position wave for a particle yields the space frequency wave of the particle in the same way that the Fourier transform of a picture gives you the spatial frequency of that picture.
We can then relate the spatial frequency of a photon to its momentum by the formula p = h * f / c, where h and c are the Planck constant and the speed of light in a vacuum, respectively. From this we see that the momentum of a photon is a function of frequency, which, from the properties of the Fourier transform, we know to be the conjugate pair of position.
First part makes sense to me. But second part doesn't. I remember learning and successfully using the p=h* f/c formula in high school physics, but what is the justification for this?
And if the formula only holds for photons, why can we say that frequncy = constant * momentum for other particles?
> Why is the fourier transform of position equal to momentum?
That comes out of the way you get the probability distribution of the position and the probability distribution of the momentum out of the wave function.
If you do the math, then one turns out to be the fourier transformation of the either. (And of course the article skipped over this, because it needs quite a bit of math).
Of course this then begs the question why there are wave functions, and why you get the position and momentum from the wave function in that particular way. And I guess the only answer I have to that is "that's how quantum mechanics works, and it matches what we observe".
> More generally, why would the fourier transform of an observable be another observable?
Again, that comes out of how you calculate particular observables from the wave function. Like above, if you do this for the energy probability distribution and the time probability distribution, they turn out to be related.
And it's not the case for any observables you can compute. For example, the energy and position are NOT fourier transforms of each other.
Energy and time are conjugate variables, not energy and position. And as we would expect, energy is the fourier transform of phase. This is why E=hf. Frequency just measures the rate of phase change akin to how momentum measures the rate of position change. As far as current knowledge goes, phase is not an observable that we can measure. Phase shift is actually a gauge symmetry in electromagnetism.
That's not how it works. When you incorporate, the corporation has shares split among the founders. The founders themselves determine the "par" value of each share - essentially its intrinsic worth.
You have to pay this amount of money to acquire the shares upon incorporation. (Each state does it a little differently.) So it's generally made a very low value between $0.0001 and $0.01. You'd pay the same amount if you were to incorporate a new business. That's it. He put some of his founding shares in Paypal in the Roth IRA when he founded the company and he got incredibly lucky. Nothing sinister happened.
Except if these were founder shares, he would likely be disqualified. "Disqualified person...an officer, director (or an individual having powers or responsibilities similar to those of officers or directors), a 10 percent or more shareholder, or a highly compensated employee (earning 10 percent or more
of the yearly wages of an employer)"
(2)Disqualified person
For purposes of this section, the term “disqualified person” means a person who is—
(A)a fiduciary;
(B)a person providing services to the plan;
(C)an employer any of whose employees are covered by the plan;
(D)an employee organization any of whose members are covered by the plan;
(E)an owner, direct or indirect, of 50 percent or more of—
(i)the combined voting power of all classes of stock entitled to vote or the total value of shares of all
classes of stock of a corporation,
(ii)the capital interest or the profits interest of a partnership, or
(iii)the beneficial interest of a trust or unincorporated enterprise,
which is an employer or an employee organization described in subparagraph (C) or (D);
(F)a member of the family (as defined in paragraph (6)) of any individual described in subparagraph (A),
(B), (C), or (E);
(G)a corporation, partnership, or trust or estate of which (or in which) 50 percent or more of—
(i)the combined voting power of all classes of stock entitled to vote or the total value of shares of all
classes of stock of such corporation,
(ii)the capital interest or profits interest of such partnership, or
(iii)the beneficial interest of such trust or estate,
is owned directly or indirectly, or held by persons described in subparagraph (A), (B), (C), (D), or (E);
(H)an officer, director (or an individual having powers or responsibilities similar to those of officers or
directors), a 10 percent or more shareholder, or a highly compensated employee (earning 10 percent or more
of the yearly wages of an employer) of a person described in subparagraph (C), (D), (E), or (G); or
(I)a 10 percent or more (in capital or profits) partner or joint venturer of a person described in
subparagraph (C), (D), (E), or (G).
The Secretary, after consultation and coordination with the Secretary of Labor or his delegate, may by
regulation prescribe a percentage lower than 50 percent for subparagraphs (E) and (G) and lower than 10
percent for subparagraphs (H) and (I).
I was surprised by that also and asked a friend who has a CPA, but doesn't work in tax law. Their first comment after briefly scanning the legal code is that "disqualified person" is only used within the context of "prohibited transaction". The definition of "prohibited transaction" concerning "disqualified person" doesn't seem to address this case. Instead, it seems to focus on dealing with the Roth IRA assets in a manner to benefits ones accounts outside of the Roth.
I don't know if that's a distinction with a difference. The rules are that they don't want you investing in a business you have material control over, as part of your IRA. Maybe it's because they think it's too risky, or can lead to self-dealing abuses...or $5 Billion tax loopholes.
The guidance they give you may be helpful
Department of Labor (DOL) Advisory Opinions suggest that under the following circumstances, a prohibited transaction would likely occur:
The transaction is part of an agreement by which an IRA owner causes IRA assets to be used in a manner designed to benefit the IRA owner (or any person in which the IRA owner has an interest) such that it would affect the exercise of the IRA owner's best judgment as an IRA fiduciary.
The IRA owner receives or will receive compensation from the subject company.
By the terms or nature of the transaction, a conflict of interest exists between the IRA and the IRA owner (or persons in which the IRA owner has an interest).
The IRA owner will be relying upon or otherwise be dependent upon the IRA investment in order for the IRA owner (or persons in which the IRA owner has an interest) to undertake or to continue the investment (e.g., minimum investment to be satisfied jointly by the IRA and IRA owner).
I'd guess $.001 is the par value and there was no 409A valuation. The initial basis doesn't really matter if it is essentially zero or $1 or $5 in this case. The implied current price on the founders shares is approximately $2500.
I agree with Propublica's take
Yet, from the start, a small number of entrepreneurs, like Thiel, made an end run around the rules: Open a Roth with $2,000 or less. Get a sweetheart deal to buy a stake in a startup that has a good chance of one day exploding in value. Pay just fractions of a penny per share, a price low enough to buy huge numbers of shares. Watch as all the gains on that stock — no matter how giant — are shielded from taxes forever, as long as the IRA remains untouched until age 59 and a half. Then use the proceeds, still inside the Roth, to make other investments.
I also think that there should be a cap on tax free distributions sheltered by Roths, and they should not be transferable upon death.
I disagree with ProPublica's take. If it was as simple as "pay just fractions of a penny per share... watch as all the gains..." then we would all do it. Not just with Roth IRAs, but with our entire portfolios. The reason we don't all do this is because startups are very very risky. Some people will succeed and walk away with windfalls. Other people will lose their shirts. If there was arbitrage, there would be a an "app for that" and there would be more billionaires walking around.
What they seem to be suggesting is that a fair valuation (well reasoned given all information) of the shares would have put the investment at millions of dollars, but due to a peculiarity of historical accounting, they could be put at worth $2K because that was the creation price and the last print.
For instance, it might be that a funding round was about to happen. This is never a sure thing, so you could claim that the shares are not worth the full price (and in any case the only trade was at 2K), while privately thinking "hmm, my shares are now worth x millions".
You then sell the shares to the Roth, thinking yourself that you're putting x millions in the vehicle while reporting 2K.
Doesn't sound illegal to me, but it also doesn't sound like things are supposed to work this way.
Forcing all IRA investment through publicly listed companies sounds like exactly the law a hedge fund would write. Why allow people to invest in assets you can own without going through a Wall Street investment bank?
Regulatory capture is forcing the entire economy through your cartel in the name of nominal protection.
Publicly listed companies are equally available opportunities for anyone participating in the contribution rate-limited game of Roth IRA maximization.
Private share contributions give huge asymmetric upside to private investors/founders. Yes they take risk in that their shares still have to end up being worth something one day, but clearly the upside tax advantages are ridiculously unbalanced against the middle class because not everyone has access to early stage investments.
So, even the playing field by:
- Letting anyone invest in early stage companies (this has many other implications)
You can buy publicly traded companies without going through brokers/stock exchanges.
What can be assured is that the exchange can be booked at a market value, which can never be guaranteed in a private sale in an opaque market, risking shenanigans to shift value beyond the contribution limit.
(You can say a corp’s initial shares have zero value, but we can all agree here that a Corp formed to execute on a startup team’s plan/idea absolutely does have value).
> The key here is that if you have to reliably identify exactly which startup to put your $2000 in.
No. Theil was already making a risky startup bet, so the "reliably identify" point is moot. All this maneuver did was let him avoid all the taxes he'd owe if it paid off.
No, the key is being able to sell yourself something for far less than its actual value so that you can squeeze millions of dollars worth of assets into the few thousand dollar contribution limit for an IRA.
All shares issued at founding have a near-zero cost because, while you technically need to buy the shares, the company (by definition) is worth $0 on the day you start it.
There is no tax gimmick involved in that part. If you require entrepreneurs to buy shares of their own company for large sums of money on the day they start the company, it would dissuade many entrepreneurs. On the day I incorporated my company in Delaware, my debt exceeded my assets and the startup was going to be my only profession.
Sure - there's no problem with valuing those shares at $0.001 in general, because there's not much that valuation matters for in the short term (eventually you will pay different taxes depending on the end result of your company).
However, Roth IRAs specifically are a tax shelter and have contribution limits, so valuations matter a whole lot for them (difference in $0.01 per share vs $0.001 per share would be a difference of $500M vs $5B today). That's why I think illiquid (or non-market cleared) securities should not be allowed in Roth IRAs.
> the company (by definition) is worth $0 on the day you start it.
Is it?
If Elon Musk forms a corporation tomorrow, its market value is more than $0 before he does a single thing with it.
And that’s all the IRS should care about for Roth contribution limits: market value.
If I buy 1000 shares of PayPal from my mom for $2000 (mkt value: a lot more!) and put that into my IRA and tell the IRS that $2000 is the price we agreed (in the marketplace of the dinner table).
If, at the moment of formation, the company has a binding agreement with Elon Musk (the founder) requiring their services for a fixed time allocation and at a fixed rate of remuneratin, then yes that contract has value and therefore the company has value. The value will depend on the remuneration to Mr. Musk vs the perceived value of his services. Even so, it would be as one of a small % of outliers with high-value founders amongst the millions of companies incorporated every year. Was Peter Thiel as valued when he started paypal as he is now? No.
More importantly, acknowleding that very few companies may have value at inception due to the value (and commitment) of their founders' time doesn't make it any easier to systematically value that time. To legally enforce this, you would have to have valuation and audit service providers who do this - creating a bureaucratic hurde that every founder - famous or not has to go through - just to start a company.
It is my opinion that the cost of doing this - in reducing or slowing down the number of companies started and the lost taxes as a result - would significanty outweigh any gain in taxes from taxing the notional value of Elon Musks's presence as part of his own company.
All laws that apply to humans, particular compliance related laws, have significant second order effects. The second order effect of taxing the popularity of folks when they start a company is that thousands of less rich, less popular, less privileged, and less confident first time founders will face an additional hurdle when starting a business and they may never start one, never get rich through one. Ultimately, inequality would likely increase and rich established founders like Elon Musk and Peter Thiel would likely be more entrenched and benefit more from this, not less.
> If Elon Musk forms a corporation tomorrow, its market value is more than $0 before he does a single thing with it.
If there’s anyone stupid enough to value such a company at more than $0, Elon should sell that company and just start another one. Infinite money machine. He should call it Bitcoin or NFT or something similar...
People will throw money at a company that has done nothing solely based on the people behind it.
I mean, people throw their money at companies that actively burn money with unlikely prospects of overcoming their death spiral. One that hasn’t even started should at least be worth much much more than those.
When the company is formed the valuation is genuinely very small because it has no assets, customers, etc. Buying some of your shares in a Roth IRA at this point is relatively common, enough so that I've heard multiple people suggest that founders do it.
Are you saying that Peter Thiel should have known that he would turn PayPal into a multibillion dollar business, and because of this, the shares were not really worthless?
EDIT: That was sarcastic, but re-reading, that basically is what the article is saying:
> Get a sweetheart deal to buy a stake in a startup that has a good chance of one day exploding in value.
As a founder you can grant yourself options or shares at essentially infinitesimally small values in the very early days of the company and pay virtually no tax.
Other countries only allow shares of publicly traded companies to be added to tax shelter savings accounts. This seems like a reasonably fair way to prevent people with significant resources from taking advantage of the system in ways the general public cannot. Someone getting returns in excess of hundreds of thousands of percent should be able to afford paying a few percent in tax to help pay for the infrastructure society has provided to make success in industry possible.
Forgive my ignorance but I was under the impression this was startup founders standard operating procedure.
1. Form a C Corp
2. Grant founders shares at $0.000x/share
3. Early exercise all of said shares at basically nothing
4. Make 83(b) election to IRS
5. Take advantage of long term cap gains and qsbs
I’m sure plenty of folks in this forum have done similar things, the only difference is mr. thiel put it into his Roth account, essentially betting on himself and it paid off big time.
You are missing the point the article. Author is not trying to argue that AI is 'harder' than physics, like a freshman cs major might argue with their physics friends.
Author is talking about how our physical theories, such as QFT, currently have more predictive power than any theories we currently have about machine learning/deep learning.
While QFT makes some amazingly precise predictions in certain areas like the fine structure constant, it is nearly useless for predicting even most chemistry.
In practice, the computations required to use the QFT model are just too complex for modern computers when it comes to single atoms with more than a few protons, not to mention larger molecules. Instead, we must use simplified models like the Bohr model to make predictions about molecular bonds.
This actually seems to be very similar to AI where we understand not everything, but a lot about basic neurons, yet the emergent phenomena of intelligence is very difficult to predict due to the explosion of computational complexity.
I think the article misses the point of what physics is. It is not a collection of "sparse" models and principles, rather, it is a scientific discipline from which such models have emerged.
You will notice the article conflates the two things: physics and the known laws of physics (e.g. first para in section 1.2). Simplicity of the latter does not imply simplicity of the former, but the article assumes that it does in order to tackle/state the question as posed: "Why is AI hard and physics simple?".
IMO if all it takes is a few simple substitutions like “physics” -> “known laws of physics” to make the article or title make sense, then it’s unfair to say that the author has missed the point. C.f. Reading the strongest possible interpretation and all that.
The title is 'clickbait' for sure, but not neccessarily incorrect. After all 'simple' can mean different things to different people. And the author clarifies what he means by 'simple' in the rest of the article.
I read TFA, hence the reference to intuition. There is nothing in the article that makes a compelling case of physics being simple, other than rhetoric.
We forget at our peril the Michelson-Morley Experiment and the Ultraviolet Catastrophe, and if we forget these, we may assume now too that we have it all figured out.
Of course, active researchers in the subject, both theoretical and experimental, do not forget.
Titles have to be short, and as such they can't hope to represent the contents of the article completely accurately.
If you wanted to do that you would have to make the title equal to the article's contents.
Based on the parts which I've read so far, a more accurate title would be 'Why some currently hot parts of AI not well understood, and some parts of Physics well understood?'
I think the original title is an ok approximation of this.
